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(D) The number of ways to choose $8$ questions from $10$ in part $A$ is given by $C(10, 8)$.The number of ways to choose $5$ questions from $10$ in pa

Vedclass · Accepted Answer

$11340$

Vedclass · Answer

(D) The number of ways to choose $8$ questions from $10$ in part $A$ is given by $C(10, 8)$.The number of ways to choose $5$ questions from $10$ in part $B$ is given by $C(10, 5)$.Since these are independent selections,the total number of ways is the product of the two combinations:Total ways $= C(10, 8) 	imes C(10, 5)$$= \frac{10!}{8!2!} 	imes \frac{10!}{5!5!}$$= \frac{10 	imes 9}{2 	imes 1} 	imes \frac{10 	imes 9 	imes 8 	imes 7 	imes 6}{5 	imes 4 	imes 3 	imes 2 	imes 1}$$= 45 	imes 252 = 11340$.

$A$ question paper has $2$ parts,part $A$ and part $B$,each containing $10$ questions. If a student has to choose $8$ questions from part $A$ and $5$ questions from part $B$,in how many ways can the student choose the questions?

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