Latest Infosys Aptitude Question SOLUTION: Q. How many 4 digit number are there which have exactly 3 distinct digit

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Q. How many 4 digit number are there which have exactly 3 distinct digit

Asked In Infosys Gangatharan (10 years ago)

Solved Diwakar Singh Read Solution (5)

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Diwakar Singh  (10 years ago)

9*9*8*10
for thousand place any digit 1-9 can be selected. for hundred place any digit 1-0 excluding the previous selected can be selected. for tens place any digit can be selected from remaining 9 and for the last any digit can be selected because 3 digit need to be distinct.

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Raman Ojha  (10 years ago)

9*9*8*7
ques is about no repetition.
so first place cant be zero . first digit would b (1 to 9) so total there is 9 ways to fill first place
second digit would be (0 to 9 but exepting one which is already set for a instance)so total ways again 9to be filled second digit.
simillarly
total 8 ways to fill 3rd digit
total 7 ways to fill 4th digit
so ultimately result is 9*9*8*7
second digit w

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gopal singh  (10 years ago)

As there should be 3 distinct digits in 4, the number will have 2 same digits and other 2 distinct - aabc (1123, 3477, ...)

C^3_{10}=120 - # of ways to choose 3 distinct digits out of 10;
C^1_3=3 - # of ways to choose which digit will be represented twice;
frac{4!}{2!}=12 - # of permutation of digits aabc;

C^3_{10}*C^1_3*frac{4!}{2!}=4320.

Now, out of these 4320 numbers some will start with zero, but 4-digit number can not start with zero as in this case it becomes 3 digit number. So how many out of these 4320 start with zero? As no digit has any preferences so equal numbers will start with each digit: 1/10 will start with 1, 1/10 with 2, 1/10 with 3 and so on. Thus 1/10=0.1 of 4320 will start with 0 and 0.9 of 4320 will start with digit other than zero.

TOTAL: 4320*0.9=3888.

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durga  (10 years ago)

total number of 4 digit number which is divisible by 4 ??

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ramya bayya  (10 years ago)

exactly 3 distinct digits means we should hav only the units digit same as the remaining digits, and we should not hav even 4 distinct digits

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