(iv) To find the number of selections with exactly one M and one A, we choose 1 M, 1 A, and 1 other letter from the remaining letters.
The word CAMERAMAN has the letters C, A, M, E, R, A, M, A, N.
There are 3 A's and 2 M's. We choose 1 M and 1 A, and then choose 1 more letter from the remaining 6 letters (C, E, R, N, A, M).
The number of ways to choose 1 letter from these 6 is given by:
\(\binom{4}{1} = 4\)
Thus, the number of different selections is 4.
(v) To find the number of selections with at least one M, we consider different cases:
- Case 1: 1 M and 2 other letters (not both A's). Choose 1 M and 2 from the remaining 7 letters (C, A, E, R, A, N).
\(\binom{4}{2} = 6\)
- Case 2: 2 M's and 1 other letter. Choose 1 from the remaining 7 letters (C, A, E, R, A, N).
\(\binom{4}{1} = 4\)
- Case 3: 1 M, 1 A, and 1 other letter. Already calculated as 4.
\(Total number of selections = 6 + 4 + 4 = 16.\)