A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 memorise) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
A.
380
B.
320
C.
260
D.
95
Answer :
380
Solution :
Either one boy will be selected or no boy will be selected. Also out of four members one captain is to be selected.
∴ Required number of ways $$ = \left( {^4{C_1} \times {\,^6}{C_3} + {\,^6}{C_4}} \right) \times {\,^4}{C_1} = \left( {80 + 15} \right) \times 4 = 380$$
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