There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible? Select the correct option
A) 625 B) 3840 C) 5625 D) 11520 E) 12520
since repetitions are allowed so there are 5 ways to choose the letters for the first slot, and five ways to choose for last slot   that can be like:- 5 x _ x _ x _ x 5   you still have to choose 1 digit and 2 letters between. For the letters, again, repetitions are allowed so each slot can be filled in 5 ways. For digit, it can only be filled in 3 ways. However, since the digit can be in any one of the 3 middle slots, so we multiply by 3 again:   5 x 3 x 5 x 5 x 5 or   5 x 5 x 3 x 5 x 5 or   5 x 5 x 5 x 3 x 5   so 5 x 5 x 5 x 5 x 3 x 3 = 5^4 x 3^2 = 5625.   ANSWER:5625
<result>C</result>
There is a five digit code consist of letters and digit. the code can have one digit from 1,2,3 and any four letters from A,b,c,d,e. first and last code must be a letter and all letters can be repeated. How many combinations can be possible?