QJEEM20Ma6709: JEE Main 2020 Mathematics - Class 11 JEEM20Ma6709 Solution: Total number of 6-digit numbers in which only and all the five…

Here none number repeats more than once.

We can choose the number which repeats more than once among 1, 3, 5, 7, 9 in ⁵C₁ ways.

Let number 3 repeats more than once. So six digits are 1, 3, 3, 5, 7, 9.

We can arrange those six digits in $$\frac{6!}{2!}$$ ways.

$$\therefore$$ Total six digit numbers = ⁵C₁ $$\times$$ $$\frac{6!}{2!}$$ = $$\frac{5}{2}\left(6!\right)$$