Question

In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
NCERT Solutions for Class 11th Mathematics Chapter 1 Exercise 1.6 7

Answer 1

Answer: 25 people like tennis only and not cricket.

                35 people like tennis.

Step-by-step explanation:

n(C) = 40

n(C intersection T) = 10

n(CUT) = 65

USING SET FORMULA ,

n(T) = n(CUT) - n(C) + n(C intersection T)

      = 65-40+10

       = 35.

therefore 35 people like tennis.

n(T-C) = 35-10

          = 25.

hence, 25 people like only tennis and not cricket

rate, comment and thanks if u liked my answer and if u found it useful

Answer 2

Given data is

There are a group of 65 people.

Total number of people are

$|p| = 65$

Out of those 65 number of people 40 like cricket

$|c| = 40$

These 40 people loves cricket. They can also love tennis along with cricket. But commonly these people loves cricket.

10 members love both cricket and tennis.

$|c \: intersection \: t| = 10$

From the given data we can find the number of people who loves only cricket

$|c - t| = |c| - |c \: intersection \: t| \\ = 40 - 10 \\ = 30$

Therefore the total number of people who loves only cricket is

$30$

1.Let's find the number of people who love tennis

we can find it by subtracting the total number of people with the people who loves only cricket.

$|t| = |p| - |c - t| \\ = 65 - 30 \\ = 35$

Therefore number of people who loves tennis is

$35$

2. let's find the number of people who loves only tennis.

The people who loves tennis can have the people who loves cricket as well. But those 35 number of people loves tennis in common.

To find the number of people who loves only tennis, we need to subtract the number of people who loves tennis with the number of people who loves both cricket and tennis.

$|t - c| = |t| - |c \: intersection \: t| \\ = 35 - 10 \\ = 25$

Therefore the total number of people who loves only tennis is

$25$

Finally the total number of people who loves tennis is

$35$

Out of them who loves only tennis is

$25$

#SPJ2