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 _______ . [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

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 _______ . [2023]

Ans.
(546)

$5 language courses$

$7 non-language courses$

$He can select:$

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

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

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

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

Want Us to Email you About Special Offers & Updates?