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Question

(A) Let $a, b, c$ be the number of questions answered from parts $A, B, C$ respectively,such that $a+b+c=7$ where $0 \le a \le 4, 0 \le b \le 3, 0 \le

Vedclass · Accepted Answer

$4655$

Vedclass · Answer

(A) Let $a, b, c$ be the number of questions answered from parts $A, B, C$ respectively,such that $a+b+c=7$ where $0 \le a \le 4, 0 \le b \le 3, 0 \le c \le 2$.The possible combinations $(a, b, c)$ are:$(4, 3, 0): \binom{7}{4} 	imes \binom{5}{3} 	imes \binom{3}{0} = 35 	imes 10 	imes 1 = 350$$(4, 2, 1): \binom{7}{4} 	imes \binom{5}{2} 	imes \binom{3}{1} = 35 	imes 10 	imes 3 = 1050$$(4, 1, 2): \binom{7}{4} 	imes \binom{5}{1} 	imes \binom{3}{2} = 35 	imes 5 	imes 3 = 525$$(3, 3, 1): \binom{7}{3} 	imes \binom{5}{3} 	imes \binom{3}{1} = 35 	imes 10 	imes 3 = 1050$$(3, 2, 2): \binom{7}{3} 	imes \binom{5}{2} 	imes \binom{3}{2} = 35 	imes 10 	imes 3 = 1050$$(2, 3, 2): \binom{7}{2} 	imes \binom{5}{3} 	imes \binom{3}{2} = 21 	imes 10 	imes 3 = 630$Total ways $= 350 + 1050 + 525 + 1050 + 1050 + 630 = 4655$.

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