Advertisements
Advertisements
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 a particular teacher is included?
Solution
The number of teachers = 5
Number of students = 20
The number of ways of selecting 2 teachers from 5 teachers is
= 5C2 ways.
= `(5!)/(2! xx (5 - 2)!)`
= `(5!)/(2! xx 3!)`
= `(5 xx 4 xx 3!)/(2! xx 3!)`
= `(5 xx 4)/(2 xx 1)`
= 10 ways
The number of ways of selecting 3 students from 20 students is
= 20C3
= `(20!)/(3! xx (20 - 3)!)`
= `(20!)/(3! xx 17!)`
= `(20 xx 19 xx 18 xx 17!)/(3! xx 17!)`
= `(20 xx 19 xx 18)/(3 xx 2 xx 1)`
= 20 × 19 × 3
= 1140 ways
∴ The total number of selection of the committees with 2 teachers and 5 students is
= 10 × 1140
= 11400
A particular teacher is included.
Given a particular teacher is selected.
Therefore, the remaining 1 teacher is selected from the remaining 4 teachers.
Therefore, the number of ways of selecting 1 teacher from the remaining 4 teacher
= 4C1 ways
= 4 ways
The number of ways of selecting 3 students from 20 students = 20C3
= `(20!)/(3!(20 - 3)!)`
= `(20!)/(3! xx 17!)`
= `(20 xx 19 xx 18 xx 17!)/(3! xx 17!)`
= `(20 xx 19 xx 18)/(3!)`
= `(20 xx 19 xx 18)/(3 xx 2 xx 1)`
Hence the required number of committees
= 1 × 4 × 1140
= 4560
APPEARS IN
RELATED QUESTIONS
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters
- cannot be repeated
- can be repeated
- cannot be repeated but must begin with E
- cannot be repeated but end with CAB.
The number of ways selecting 4 players out of 5 is
There are 10 true or false questions in an examination. Then these questions can be answered in
Prove that 15C3 + 2 × 15C4 + 15C5 = 17C5
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
In a parking lot one hundred, one-year-old cars, are parked. Out of them five are to be chosen at random for to check its pollution devices. How many different set of five cars can be chosen?
How many ways can a team of 3 boys,2 girls and 1 transgender be selected from 5 boys, 4 girls and 2 transgenders?
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 4 elements
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of at most 3 women?
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?
There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find, the number of straight lines that can be obtained from the pairs of these points?
There are 11 points in a plane. No three of these lie in the same straight line except 4 points which are collinear. Find the number of triangles that can be formed for which the points are their vertices?
Choose the correct alternative:
The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is
Choose the correct alternative:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines
Choose the correct alternative:
Number of sides of a polygon having 44 diagonals is ______
Choose the correct alternative:
In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is
Choose the correct alternative:
The number of rectangles that a chessboard has ______
