BTGmoderatorLU wrote:How many numbers with 3 different digits can be formed using only the odd digits?

(A) 10
(B) 20
(C) 40
(D) 60
(E) 120

The OA is D.

The first digit has 5 choices (1, 3, 5, 7, 9), then the second and third digits have 4 and 3 choices, respectively. So the total number of numbers with 3 different odd digits is:

5 x 4 x 3 = 60

Alternate Solution:

The three digits can be chosen in 5C3 = 5!/(3!*2!) = (5 x 4)/(2 x 1) = 5 x 2 = 10 ways. The chosen digits can be arranged in 3! = 3 x 2 = 6 ways. Thus, a total of 10 x 6 = 60 different numbers is possible.

Answer: D