A seven digit number is formed by using the digits 3, 3, 4, 5, 5, 8 & 9. Probability that the number

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02 Oct 2014 Probability

A seven digit number is formed by using the digits 3, 3, 4, 5, 5, 8 & 9. Probability that the number formed is great than 57,26,000 is?

OPtion

1) 3/8
2) 1/5
3) 1/3
4) 2/9
5) 12/35
6) 16/35
7) 8/35
8) 8/21
9) 2/5
10)None of these

Solution

Total no. of numbers formed by using the given digits 3,3,4,5,5,8,9 = (7*6*5*4*3*2*1)/(2*1)*(2*1) = 1260
(Denominator part is due to the repetition of 3 and 5)
Total no. of numbers formed by using the given digits 3,3,4,5,5,8,9 which are greater than 57,26,000 are of two types
Total no. of numbers started with 5 = (2*2*5*4*3*2*1)/ (2*1)*(2*1) = 120
Total no. of numbers started with 8&9 = (2*6*5*4*3*2*1)/ (2*1)*(2*1) = 360
Hence required probability = (120 + 360)/ 1260 = 480/1260 = 8/21

Correct Option: 8 Best Solution (29)

Narasapu Hari prasad   10 years AGO

total sample space is 7!/(2!*2!)=1260
total number of numbers formed by 3,3,4,5,5,8,9 which are greater than 5726000 are
when first digit is 5 second digit should be 8 or 9
so 58*****=5!/2!=60
and 59*****=5!/2!=60
or first digit should be 8 or 9
so 8******=6!/(2!*2!)=180
and 9******=6!/(2!*2!)=180
so required probability = (60+60+180+180)/1260=480/1260=8/21

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RAKESH   10 years AGO

total = 7!/2*2 = 1260

greater than 57,26,000 = 5(7/8)----- , 8------, 9-------
= 2*5!/2 + 6!/2*2 + 6!/2*2
= 120 + 180 + 180
= 480

p = 480/1260 = 8/21

Like? Yes (6) | No (1)  

Gitanjali K   10 years AGO

required probability = (120+360)/1260 =8/21

Like? Yes (3) | No   

harshit gupta   10 years AGO

OPTION 8 is correct. Here is a solution

total different no. = 7!/(2!*2!)
Now three cases are made for no. greater than 5726000

CASE 1 -- No. Starting with 8
total different no.= 6!/(2!*2!)

CASE 2 -- No. Starting with 9
total diff. no.= 6!/(2!*2!)

case 3 --No. Starting with 5
total no.= (2*5!)/2! ( since 8 &9 can come at second place)

Total no.= 6!/(2!*2!)+ 6!/(2!*2!)+ (2*5!)/2!=(2*5!+6!)/2!
Probability= ((2*5!+6!)*2!*2!)/(2!*7!)
prob= 8/21

Like? Yes (3) | No   

Chirag Ranjan Lahiri   10 years AGO

Total no. of numbers formed by using the given digits 3,3,4,5,5,8,9 = (7*6*5*4*3*2*1)/(2*1)*(2*1) = 1260

(Denominator part is due to the repetition of 3 and 5)

Total no. of numbers formed by using the given digits 3,3,4,5,5,8,9 which are greater than 57,26,000 are of two types

Total no. of numbers started with 5 = (2*2*5*4*3*2*1)/ (2*1)*(2*1) = 120
Total no. of numbers started with 8&9 = (2*6*5*4*3*2*1)/ (2*1)*(2*1) = 360
Hence required probability = (120 + 360)/ 1260 = 480/1260 = 8/21

Like? Yes (2) | No   

santosh kumar patel   10 years AGO

total no of formed=!7/!2*!2=1260
formed greater than 572600 are 2 ways
total no start from 5=120
8&9=360
hence required probability=120+360/1260=8/21
ans:8/21

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Mahesh   10 years AGO

The number of numbers that start with 58 is 5!/2!=60
The number of numbers that start with 59 is 5!/2!=60
The number of numbers that start with 8 is 6!/2!2!=180
The number of numbers that start with 9 is 6!/2!2!=180

The total possibilities= 7!/2!/2!=1260

The required probability = 480/1260=8/21

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kumar   10 years AGO

8/21

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Neel Patel   10 years AGO

In first place
By taking 8&9 there are
2*6!/(2!2!)=360
And taking 5 at first place
There 1*2*5!/2!=120

Total numbers =7!/2!/2!=1260
Prob=120+360)/1260=8/21

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MRITUNJAY KUMAR   10 years AGO

8/21

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vikash kumar   10 years AGO

tot=7!/(2!*2!)=A

ways=5!+(6!/2!*2!)+(6!/2!*2!)=B

ans:=B/A= 8/21

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vivek prakash   10 years AGO

if we start with 5 then 1st position is filled by 2 ways then 2nd placed is must filled with 8 or 9 so remaining position by !5 so if we start with 5 no ways of forming no is 2*2*!5
second case fist digit can start with 8 or 9 then no of ways of forming no is 2*!6
we no restriction then noof ways of forming no is !7
(4*!5+2*!6)/!7=8/21

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shekhar suman   10 years AGO

total no of possible outcome =7!/2!*2!
favorable outcome= 5!+2*6!/2!*2!
so p(a)=(5!+2*6!/2!*2!)*4/7!

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Karunendra Singh   10 years AGO

number will be greater than given 5726000 when first 2 position digit and 9 take place so for place one there will be two number
2*6*5*4*3*2*1
after this if we place first place digit 5 and at second place put 8 or 9 then it also will be greater than given number so for there are wo option because there are two five
2*2*5*4*3*2*1
total combination of number greater than given number =1440+480= 1920
and total number of combination of number = 7*6*5*4*3*2*1= 5040
and answer will be 5040/1920 = 8/211.........

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Vishesh Mishra   10 years AGO

for first position there will be two number that is 8 and 9 so 2*6*5*4*3*2*1= 1440 and if we place 5 at first then 2*2*5*4*3*2*1= 480 so total number of combination ie greater than given number = 1920 and total number that having 7 digit = 7*6*5*4*3*2*1= 5040 ,
answer = 5040/(1440+480)= 8/21..........

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rajeev chaubey   10 years AGO

5 8 - - - - - =5!/2!=60 numbers
5 9 - - - - - =5!/2!=60 numbers
8 - - - - - - =6!/2!2!=180 numbers
9 - - - - - - =6!/2!2!=180 numbers
60+60+180+180=480 numbers
total words formed by given numbers=7!/2!2!=1260
P=480/1260=8/21

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BalaGanesh S   10 years AGO

Total 7 digits numbers can be formed are 7!/(2!*2!)

Numbers greater than 5726000 means the numbers should start with 8 or 9 or start with 58 or 59,
i.e 8 _ _ _ _ _ _=6!/(2!*2!) +
9 _ _ _ _ _ _= 6!/(2!*2!) +
58 _ _ _ _ _ =5!/2! +
59 _ _ _ _ _ = 5!/2!

Probability = (2*6!/(2!*2!) + 2*5!/2!) / 7!/(2!*2!) = 8/21

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~Sandeep~   10 years AGO

Count of Numbers formed which are greater than 57,26,000 would be sum of=>
58* Series = 5!/2!
59* Series = 5! /2!
8* Series = 6! 2*2
9*Series = 6!/2*2
Sum= 4*5!

Total count of numbers formed using these 7 digits = 7!/(2!*2!)

Probability= (4*5!)/ (7!)/2*2 = 16/ 42 = 8/21

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urvish   10 years AGO

7C4+7C2/7C2
=8/21

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DE PRAKASH TIWARY   10 years AGO

total no of numbers formed by these digits is 7!/4. And the no of numbers greater than 5726000 is 8*5!/2

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Md.Sultan Khichi   10 years AGO

Num shud be greater than 5726000 for this num shud be start wid 58......=5!/2!=60
59.....=5!/2!=60
8......=6!/2!/2!=180
9......=6!/2!/2!=180
Total nums greater than 572600=60+60+180+180=480
And total nuns form by these digits are=7!/2!/2!=1260..
Probability=480/1260=8/21..
Ans.. 8/21

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CHANDAN KUMAR   10 years AGO

TOTAL NO. FORMED=7!/21*2!=1260
no. greater than 5726000=2*60+180*2=480
p=480/1260=8/21

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dhananjay kumar   10 years AGO

Total number greater than 572600=60+60+180+180=480
And total number=7!/2!/2!=1260..
Probability is 480/1260
Ans.. 8/21

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Rupesh Rajesh Deshmukh   10 years AGO

480/1260=8/21

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Vibha   10 years AGO

p(> 5726000) =
{ P(starting with 5) + P(starting with > 5) } /total
= 8/21

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Kushagra Tiwari   10 years AGO

Num shud be greater than 5726000
for this num shud be start wid
58......=5!/2!=60
59.....=5!/2!=60
8......=6!/2!/2!=180
9......=6!/2!/2!=180
Total nums greater than
572600=60+60+180+180=480
And total nuns form by these digits
are=7!/2!/2!=1260..
Probability=480/1260=8/21..
Ans.. 8/21

Like? Yes (1) | No   

Shreya Tiwari   10 years AGO

Num shud be greater than 5726000
for this num shud be start wid
58......=5!/2!=60
59.....=5!/2!=60
8......=6!/2!/2!=180
9......=6!/2!/2!=180
Total nums greater than
572600=60+60+180+180=480
And total nuns form by these digits
are=7!/2!/2!=1260..
Probability=480/1260=8/21..
Ans.. 8/21

Like? Yes (1) | No   

Abhishek Vishwakarma   10 years AGO

Num shud be greater than 5726000
for this num shud be start wid
58......=5!/2!=60
59.....=5!/2!=60
8......=6!/2!/2!=180
9......=6!/2!/2!=180
Total nums greater than
572600=60+60+180+180=480
And total nuns form by these digits
are=7!/2!/2!=1260..
Probability=480/1260=8/21..
Ans.. 8/21

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neha kumari   10 years AGO

no of no greater than 5726000=480
possible no=1260
p=8/21

Like? Yes (1) | No