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 eourses is

Question

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 eourses is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For at most two language courses = 5 C 2 × 7 C 3+ 5 C 1 × 7 C 4+ 7 C 5=546

Q. 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 eourses is

For at most two language courses
$=^{5} C_{2} \times^{7} C_{3} +^{5} C_{1} \times^{7} C_{4} +^{7} C_{5} = 546$

Q. 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 eourses is

For at most two language courses =5C2​×7C3​+5C1​×7C4​+7C5​=546

For at most two language courses
$=^{5} C_{2} \times^{7} C_{3} +^{5} C_{1} \times^{7} C_{4} +^{7} C_{5} = 546$