Permutation Combination Question 14

Question 14 - 30 January - Shift 2

The number of seven digits odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is __________

Show Answer

Answer: 240

Solution:

Formula: Non-Consecutive Selection

Digits are 1, 2, 2, 2, 3, 3, 5

If unit digit 5 , then total numbers $=\frac{6 !}{3 ! 2 !}$

If unit digit 3 , then total numbers $=\frac{6 !}{3 !}$

If unit digit 1 , then total numbers $=\frac{6 !}{3 ! 2 !}$

$\therefore$ total numbers $=60+60+120=240$