# EXERCISE 17.2

QUESTION 1

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can
this be done?

Sol :

Required number of ways

= 1365

QUESTION 2

How many different boat parties of 8 , consisting of 5 boys and 3 girls, can be made from 25 boys
and 10 girls?

Sol :

Clearly, out of the 25 boys and 10 girls, 5 boys and 3 girls will be chosen.

Then, different boat parties of

= 6375600

QUESTION 3

In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory
for every student?

Sol :

We are given that 2 courses are compulsory out of the 9 available courses,

Thus, a student can choose 3 courses out of the remaining 7 courses.

Number of ways

= 35

QUESTION 4

In how many ways can a football team of 11 players be selected from 16 players? How many of
these will

(i) include 2 particular players?

(ii) exclude 2 particular players?

Sol :

Number of ways in which 11 players can be selected out of 16

= 4368

(i) If 2 particular players are included, it would mean that out of 14 players, 9 players are
selected.

Required number of ways

= 2002

(ii) If 2 particular players are excluded, it would mean that out of 14 players, 11 players are
selected.

Required number of ways

= 364

QUESTION 5

There are 10 professors and 20 students out of whom a committee of 2 professors 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 professor is included.

(ii) a particular student is included.

(iii) a particular student is excluded.

Sol :

Clearly, 2 professors and 3 students are selected out of 10 professors and 20 students ,respectively.

Required number of ways

= 51300

(i) If a particular professor is included, it means that 1 professor is selected out of the remaining 9
professors.

Required number of ways

= 10260

(ii) If a particular student is included, it means that 2 students are selected out of the remaining 19
students.

Required number of ways

= 7695

(iii) If a particular student is excluded, it means that 3 students are selected out of the remaining
19 students.

Required number of ways

= 43605

QUESTION 6

How many different products can be obtained by multiplying two or more of the numbers 3 , 5 , 7
, 11 (without repetition)?

Sol :

Required number of ways of getting different products

QUESTION 7

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?

Sol :