A boy needs to select five courses from 12 av | vedclass

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(C) Total courses = $12$,Language courses = $5$,Non-language courses = $7$.We need to select $5$ courses such that at most $2$ are language courses.Ca

Vedclass · Accepted Answer

$546$

Vedclass · Answer

(C) Total courses = $12$,Language courses = $5$,Non-language courses = $7$.We need to select $5$ courses such that at most $2$ are language courses.Case $1$: $0$ language courses and $5$ non-language courses:$^{5}C_{0} 	imes ^{7}C_{5} = 1 	imes 21 = 21$.Case $2$: $1$ language course and $4$ non-language courses:$^{5}C_{1} 	imes ^{7}C_{4} = 5 	imes 35 = 175$.Case $3$: $2$ language courses and $3$ non-language courses:$^{5}C_{2} 	imes ^{7}C_{3} = 10 	imes 35 = 350$.Total ways = $21 + 175 + 350 = 546$.

$A$ boy needs to select five courses from $12$ available courses,out of which $5$ courses are language courses. If he can choose at most two language courses,then the number of ways he can choose five courses is

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