Question

There are 5 teachers and 20 students. Out of them a committee of 2 teachers and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees (i) a particular teacher is included? (ii) a particular student is excluded?
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Answer 1

select 2 teachers out of 5= 5c2

selecting 3 students out of 2p = 20c3

no. of ways of selecting 2 teachers and 3 students = 5c2×20c3

= 10×20×19×18/6 = 11400

i) one particular teacher is included

no of teachers = 5-1 =4

no of teachers to select is 2-1 =1

4c1 ×20c3 = 4560

ii) a particular student excluded

no of students = 20-1 =19

no of students to select = 3

5c2× 19c3

= 10×19×18×17/6 =9690