| A committee of five members is to be formed out of 3 trainees, 4 professors and 6 research associates. In how many different ways this can be done, if the committee should have all the 4 professors and 1 research associate or all 3 trainees and 2 professors? |
A) 15
B) 18
C) 25
D) 12
E) Other than those given as options
Correct Answer: D
Solution :
| Required number of ways |
| \[={}^{4}{{C}_{4}}\times {}^{6}{{C}_{1}}+{}^{3}{{C}_{3}}\times {}^{4}{{C}_{2}}\] |
| \[=1\times 6+1\times 6=12\] |
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