From 4 gentlemen and 6 ladies a committee of five is to be selected. The number of ways in which the committee can be formed so that gentlemen are in majority is
A.
66
B.
156
C.
60
D.
None of these
Answer :
66
Solution :
The committee will consist of 4 gentlemen and 1 lady or 3 gentlemen and 2 ladies.
∴ the number of committees $$ = {\,^4}{C_4} \times {\,^6}{C_1}{ + ^4}{C_3} \times {\,^6}{C_2}.$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is