Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys $$A$$ and $$B,$$ who refuse to be the members of the same team, is:
A.
500
B.
200
C.
300
D.
350
Answer :
300
Solution :
Since, the number of ways to select 2 girls is $$^5{C_2}.$$
Now, 3 boys can be selected in 3 ways.
(1) Selection of $$A$$ and selection of any 2 other
boys (except $$B)$$ in $$^5{C_2}$$ ways
(2) Selection of $$B$$ and selection of any 2 two other
boys (except $$A)$$ in $$^5{C_2}$$ ways
(3) Selection of 3 boys (except $$A$$ and $$B)$$ in $$^5{C_3}$$ ways
Hence, required number of different teams
$$ = \,{\,^5}{C_2}\left( {^5{C_2}{ + ^5}{C_2}{ + ^5}{C_3}} \right) = 300$$
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