A candidate is required to answer 6 out of 12 | vedclass

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Question

(A) The candidate must select a total of $6$ questions from two parts,$A$ and $B$,with the constraint that no more than $4$ questions can be selected

Vedclass · Accepted Answer

$850$

Vedclass · Answer

(A) The candidate must select a total of $6$ questions from two parts,$A$ and $B$,with the constraint that no more than $4$ questions can be selected from either part. The possible combinations are as follows:   Part $A$ Part $B$   $4$ questions $2$ questions   $3$ questions $3$ questions   $2$ questions $4$ questions   The total number of ways is given by: $Ways = ({ }^{6}C_{4} 	imes { }^{6}C_{2}) + ({ }^{6}C_{3} 	imes { }^{6}C_{3}) + ({ }^{6}C_{2} 	imes { }^{6}C_{4})$ $Ways = (15 	imes 15) + (20 	imes 20) + (15 	imes 15)$ $Ways = 225 + 400 + 225$ $Ways = 850$

$A$ candidate is required to answer $6$ out of $12$ questions which are divided into two parts $A$ and $B$,each containing $6$ questions. The candidate is not permitted to attempt more than $4$ questions from any part. In how many different ways can he/she make his/her choice of $6$ questions?

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