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

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21 Jan 2010 number greater then 57,26,000?

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) 8/21
4) 2/9
5) 12/35
6) 16/35
7) 8/35
8) 1/3
9) 2/5
10) 9/35

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: 3 Best Solution (7)

Aman   14 years AGO

Total number of permutations of the given numbers = (7!/2!*2!) = 1260

The numbers greater than 5726000 can be:
1)58*****, Number of possibilities = 5!/2! = 60
2)59*****, Number of possibilities = 5!/2! = 60
3)8******, Number of possibilities = (6!/2!*2!) = 180
4)9******, Number of possibilities = (6!/2!*2!) = 180

Therefore, reqd probability = (60+60+180+180)/1260 = 480/1260 = 8/21

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hitesh gakhar   14 years AGO

total no.s formed are 1260...
no.s greater than 5726000 are 480...
prob is 480/1260=8/21

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Dimple   14 years AGO

Total possible numbers = 1260

Numbers starting with first digit as 5 and second digit as 8 or 9 = 120
Numbers starting with 8 or 9 = 360

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

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Saranjit Singh   14 years AGO

For the number formed will be greater than 57,26,000 there are two cases
1. the most significant digit will be greater then 5.....
2. the two most significant digits will be greater then 57........
.
.
probability of case 1 = 2/7 (as out of seven digits there are two digits 8 and 9 which is greater then 5)
.
.


probability of case 2 = (probability of first digit = 5) * (probability of second digit > 7)
probability of case 2 = (2/7)*(2/6)
.
.
probability of the number formed will be greater than 57,26,000 = probability of case 1 + probability of case 2
= (2/7) + (2/7)*(2/6)
= 8/21

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kewal   14 years AGO

480/1260= 8/21

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Dr.Dipin Singh   14 years AGO

Total possible numbers = 1260
.
.

Total possible numbers greater than 5726000 = 120+360 = 480 ....................

Probabilty = 480/1260 = 8/21 .. option 3

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susmit   14 years AGO

THERE ARE 2 CASES. 1) FIRST DIGIT IS 5 2)FIRST DIGIT IS 8 OR 9. CASE 1) THERE ARE 2 POSSIBLITIES FOR FIRST DIGIT AND 2 FOR THE SECOND DIGIT THEN FOR REMANING DIGITS THERE ARE 5 FACTORIAL WAYS. CASE 2) THERE ARE 2 POSSIBLITIES FOR FIRST DIGIT AND THEN THERE ARE 6 FACTORIAL WAYS.ALSO TOTAL NO. OF WAYS IS 7 FACTORIAL.THEREFORE ANSIS (4*5!+2*6!)/7!=(2/21+2/7)

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