Revisiting combinatorics 1!

Find the number of six digit numbers in which exactly two digits are even.

if your answer is N

then report the nearest integer to N/10000


The answer is 22.

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1 solution

Zee Ell
Nov 2, 2016

The number of values, where the first digit is odd (5 choices for each of the 6 digits, as there are 5 even and 5 odd digits, we can choose the position of the 2 even digits out of 5 (except the first digit)) :

( 5 2 ) × 5 6 = 156250 { 5 \choose 2} × 5^6 = 156250

The number of values, where the first digit is even (4 choices for the first digit (as there are 4 even digits different from 0), 5 choices for the rest of the 5 digits each; the position of the other even digit can be chosen 5 ways):

4 × 5 × 5 5 = 62500 4 × 5 × 5^5 = 62500

The total number of suitable values:

156250 + 62500 = 218750 156250+62500 = 218750

Hence, our answer should be:

218750 10000 = 21.875 = 22 (0 d. p.) \frac {218750}{10000} = 21.875 = \boxed { 22 \text { (0 d. p.) } }

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