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6.Permutation and Combination
medium
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
$140$
B
$196$
C
$280$
D
$346$
Solution
(a) Number of ways for select $4$ Questions out of $5$ Questions.
Number of ways $ = \,{\,^5}{C_4} = 5$
Remaining Questions =$8$
Remaining Questions for solving =$6$
Number of ways ${\,^8}{C_6} = 28$
Number of total ways ${ = ^5}{C_4} \times {\,^8}{C_6}$ $ = 5 \times 28$ $ = 140$.
Standard 11
Mathematics
