let me know detailed process of solving this problem 3 Suppo

let me know detailed process of solving this problem

3. Suppose each student in M118 is to be assigned a code number which starts with a letter from the set (A, B, C, D, E,F) and then is followed by 3 digits each from the set H1,2, 3, 4, 5, 6). For example, B-3-4-3 is one such code. How many such codes exist? (a) 6 x P(7,3) (b) 64 (c) 6 x 7 (d) 6 x C(7, 3) e) none of the others

Solution

Here The first letter is filled by alphabets {A,B,C,D,E,F} in 6 ways

3 digit number is filled by {1,2,3,4,5,6} numbers each one having 6 ways.

i.e. 6X6X6= 6^3 ways.

Finally total ways are filling are = 6X6^3= 6^4 ways