If the number of five digit numbers with distinct digits and 2 at the $10^{\text {th}}$ place is 336 k , then k is equal to:

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Permutations and Combinations

If the number of five digit numbers with distinct digits and 2 at the

1 0^{th}

place is 336 k , then k is equal to:

Answer: (D)

The five-digit number has

2

fixed in the tens place. The leading digit cannot be

0

2

, giving

8

choices, and the remaining three places take distinct digits from those still available, giving

8

7

and

6

choices. The count is

8 \times 8 \times 7 \times 6 = 2688

, and setting

2688 = 336 k

gives

k = 8

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option