Question

Permutation and combination:
how many different 7 digit numbers are there the sum of whose digits are odd?
options: a)45*10^5, b) 24*10^5, c)224320, d)none of these
correct ans : (a)

Answer 1

what are the answer choices

Answer 2

7 digit number is of the form abcdefg. In this the sum of the digits would end up as a even number only if the following is true.

a) There number of even number among these numbers -- a, b, c, d, e, f and g should be either 1 or 3 or 5 or 7.

Also the number of even and odd single digit numbers are 5. (1,3,5,7,9 and 0, 2, 4, 6, 8)

To summarize, let us take the even digit to be e and odd digit to be o.

Hence the number abcdefg could be either

ooooooe OR ooooeee OR ooeeeee OR eeeeeee

Number of ways to choose a even or odd digit is 5.

Hence answer is 4*5^7.

Answer 3

ans is: 45 * 10^5
options are: 45*10^5, b) 24*10^5, c)224320, d)none of these