First slide

Permutations

Question

Total number of 6-digit numbers in which only one digit of 1,3,5,7 and 9 can be repeated and all the five digits 1, 3, 5, 7 and 9 appear is:

Easy

A

$\frac{5}{2} (6!)$
B

$\frac{1}{2} (6!)$
C

$5^{6}$
D

$6!$

Solution

1,3,5,7,9
          For digit to repeat we have   $^{5} C_{1}$ choice
          And six digits can be arrange in   $\frac{6}{2}$ ways
          Hence total such number = $\frac{56}{2}$

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