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

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 courses is ________.

Smart Achievers · Accepted Answer

(546)

5 language courses and 7 non-language courses.

He can select:

(i) 0 language courses and 5 non-language courses in ${}^{5}C_{0} \times {}^{7}C_{5} = 21$ ways

(ii) 1 language course and 4 non-language courses in ${}^{5}C_{1} \times {}^{7}C_{4} = 175$ ways

(iii) 2 language courses and 3 non-language courses in ${}^{5}C_{2} \times {}^{7}C_{3} = 350$ ways

Required number of ways $= 21 + 175 + 350 = 546$ ways.

Solution

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 courses is ________.

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Solution

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 courses is ________.

Want Us to Email you About Special Offers & Updates?

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 courses is ________.