A candidate is required to answer 6 out of 10 | vedclass

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Question

(D) There are $10$ questions in total,divided into two groups,$A$ and $B$,each containing $5$ questions. The candidate must answer $6$ questions in to

Vedclass · Accepted Answer

$200$

Vedclass · Answer

(D) There are $10$ questions in total,divided into two groups,$A$ and $B$,each containing $5$ questions. The candidate must answer $6$ questions in total,with a maximum of $4$ questions from each group.The possible combinations of questions from Group $A$ and Group $B$ are:Group $A$Group $B$$4$$2$$3$$3$$2$$4$Therefore,the total number of ways to choose the questions is:$= {}^{5}C_{4} 	imes {}^{5}C_{2} + {}^{5}C_{3} 	imes {}^{5}C_{3} + {}^{5}C_{2} 	imes {}^{5}C_{4}$$= (5 	imes 10) + (10 	imes 10) + (10 	imes 5)$$= 50 + 100 + 50 = 200$

$A$ candidate is required to answer $6$ out of $10$ questions,which are divided into two groups each containing $5$ questions. The candidate is not permitted to attempt more than $4$ questions from each group. In how many ways can the candidate make their choice?

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