A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
A.
346
B.
140
C.
196
D.
280
Answer :
196
Solution :
As for given question two cases are possible.
(i) Selecting 4 out of first five question and 6 out of remaining 8 question $$ = {\,^5}{C_4} \times {\,^8}{C_6} = 140{\text{ choices}}{\text{.}}$$
(ii) Selecting 5 out of first five question and 5 out of remaining 8 questions $$ = {\,^5}{C_5} \times {\,^8}{C_5} = 56{\text{ choices}}{\text{.}}$$
Therefore, total number of choices $$ = 140 + 56 = 196.$$
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