Total number of 6 - digit numbers in which only and all the five digits 1 , 3 , 5 , 7 and 9 appears, is

Step-by-step solution

As we have to make a six-digit number by using all the digits 1 ,   3 ,   5 ,   7 ,   9 , hence exactly one of the digits is repeating. For the digit to repeat we have 5 C 1 = 5 choices. And, six digits in which one is repeating can be arranged in 6 ! 2 ! ways. Hence, total such numbers = 5 × 6 ! 2 ! = 5 2 6 ! .