Latest Microsoft Aptitude Question SOLUTION: How many 4 digit numbers even have no repeted digits

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How many 4 digit numbers even have no repeted digits

Asked In Microsoft PARAG KAMRA (10 years ago)

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ashish ranka  (10 years ago)

when unit digit contain 0 then
9*8*7*1(0)=504
when unit digit not contain 0
then
8*8*7*4(2,4,6,8)=1792
1792+504=2296

Is this solution Helpfull? Yes (16) | No   

Sajib Ghosh  (10 years ago)

we can't place 0 in the first position.
so, in the first position 9 no. of ways we can place a digit.
but, in the second position we can place 0 but not the 1st digit's no.
so, in the second position 9 no. of ways we can place a digit.
similarly, in 3rd and 4th position 8 and 7 no. of ways respectively.
so, total no. of ways-->> 9*9*8*7=4536

Is this solution Helpfull? Yes (7) | No (3)  

ROSHAN KUMAR  (10 years ago)

9*8*7[0]+4*8*8*7[2,4,6,8]=2296

Is this solution Helpfull? Yes (5) | No (2)  

naresh ch  (10 years ago)

9*8*7(0)----possibility 1
8*9*7(2)-------" 2
8*7*9(2)-------" 3
8*9*7(4)-------" 4
8*7*9(4)-------" 5
8*9*7(6)-------" 6
8*7*9(6)-------" 7
8*9*7(8)-------" 8
8*7*9(8)-------" 9
total=9*9*8*7=4536

Is this solution Helpfull? Yes (3) | No (2)  

ramcharan reddy  (10 years ago)

9*9*8*7
1st digit must not be zero.so,1-9
2nd digit 0-9(but repetion not allowed so 9)
nd so on

Is this solution Helpfull? Yes (2) | No (1)  

radhe shyam  (10 years ago)

2296 is correct

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Kirtiwardhan Tandale  (10 years ago)

9*9*8*7 = 4536

Is this solution Helpfull? Yes (1) | No (1)  

rajat  (10 years ago)

1680= 8*7*6*5

Is this solution Helpfull? Yes (1) | No (1)  

Vijay Pratap Singh  (9 years ago)

For even numbers the unit digit can be only 0 2 4 6 8
so, 9*8*7*1(0) = 504
8*8*7*1(2) = 448
8*8*7*1(4) = 448
8*8*7*1(6) = 448
8*8*7*1(8) = 448

total = 448*4 + 504 = 2296

Is this solution Helpfull? Yes (1) | No   

vignesh_thangaraj  (10 years ago)

10*9*8*7=5040

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rajat  (10 years ago)

2240=8*8*7*5

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AMIT KUMAR  (10 years ago)

1st digit fill with 9 way
2nd digit fill with 8
3rd with 7
4th with 6
total no.==9*8*7*6=3024 no. ans.

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anoop kumar  (10 years ago)

for a number to be even number it should contain either 0,2,4,6,8 in units place so units place can be filled in 5 ways.
in thousands place 0 should not be included so 8 ways can be filled in thousands place.
in hundreds place including 0 8 ways are possibe,in tens place 7 ways are possible total 2240 ways

Is this solution Helpfull? Yes | No (1)  

Shivam Gandhi   (10 years ago)

let w={0,1,2,3,4,5,6,7,8,9}
thousandth place has 9 possibilities : w-{0}
hundredth place has 9 possibilities : w-digit on thousandth place = set u
tenth place has 8 possibilities : u-digit on hundredth place = set v
ones place has 7 possibilities : v-digit on tenth place
Therefor, answer = 9*9*8*7=4536

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sindhura  (10 years ago)

_ _ _ _
1 2 3 4
In first position 0 cannot be placed . So we can place any number from 1 to 9 in 9ways
In the remaining 3 places , the remained 9 places can be filled in [(9.8.7)/3.2].3.2 ways ..
hence answer is 9.9.8.7=4536

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lokesh babu  (10 years ago)

Even Numbers having a single digits are 2 4 6 8.
so number of four digits without any repetition are 4x3x2x1=24.

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santhi   (9 years ago)

ans:120
even=0,2,4,6,8
5*4*3*2=120

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Aayushi Porwal  (9 years ago)

2296
if the last place is filled by 2or 4 or 6or 8 then the last place has 4 options first place has 8 options(it can't be 0 and no repeatition allowed therefore one of last digit is left),2nd posion can be filled by 8 digits and 3rd by 7 digits making equal to 1792.Another case if we consider last digit to be filled by 0 then 1st digit has 9 options,2nd position have 8 options and 3rd position has 7 options making equal to 504 and hense the ans 2296

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tharun  (9 years ago)

Total number of N.O with zero not a starting element: 9*9*8*7=4536
Total number of odd elements staring with no zero: 8*8*7*5=2240
subtract both->2296 even numbers with zero not as starting element

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PULLALHANAM B.V.M SAI SUDHEER  (9 years ago)

Last digit must be filled with (0,2,4,6,8)since even no. And 1st place must not be 0 and (9-1) so 8 can be allowed and in sane way and 3 also 8 ways totally (8*8*8)*(4c1)=2048 i think....

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Sumit Sharma  (9 years ago)

2240
last digit have 5 choices that are 2,4,6,8,0.
first digit can be any digit except 0,so for first digit we have 8 choices(excluding 0 and digit on last palce).
rest two digits have 8 and 7 choices as the digits are not repetitive.

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souharda  (9 years ago)

7*8*9*5=2520

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Asha  (9 years ago)

Probability for no repeated digits : 10*9*8*7=5040
But if zero comes in first place (i.e thousand's place) it will become a 3 digit number so excluding the probability of its occurrence : 9*8*7=504
Answer: 5040-504-4536

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sunandini vutturi  (7 years ago)

1020
9*8*7*5C1

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