Question

If the number of five digit numbers with distinct digits and 2 at the 10 t h place is 336 k , then k is equal to:

A. 8
B. 7
C. 4
D. 6

Answer 1

The number of five-digit numbers with distinct digits and 2 at the 10th place is 8 × 9 × 8 × 7 = 4032. Solving for k gives k = 12. The correct answer is A. 8.

Step-by-step explanation:

The number of five-digit numbers with distinct digits and 2 at the 10th place can be found by considering the available options for the remaining four digits.

Since the digits must be distinct, the first digit can be any number except 0 and 2 (to avoid repetition). This leaves 8 options. The remaining three digits can be any number from 0 to 9, except for the digit already used and 2 (to maintain distinctness).

So, the total number of five-digit numbers with distinct digits and 2 at the 10th place is 8 options for the first digit × 9 options for the second digit × 8 options for the third digit × 7 options for the fourth digit = 8 × 9 × 8 × 7 = 4032.

Now, if we have 336k such numbers, then 336k = 4032. Solving for k gives k = 4032 / 336 = 12.

Therefore, k is equal to 12.