Maths NCERT Solutions Class 11

Maths NCERT Solutions Class 11 - Permutation

Class 11 maths: - Example: A family goes to a studio to have their photo taken, and the photographer must arrange them to get the best shot. Three of them have red shirts, four of them have blue shirts, and two of them have black shirts. How many ways can the photographer arrange the family members?

In this example, there are 9 family members total, regardless of shirt color, so the n value is 9. In the denominator the 3 family members wearing red would be the n1 value, the 4 family members wearing blue would be the n2 value, and the 2 family members wearing black shirts would be the n3 value.

P=9! / 3! *4! *2!

In the numerator, 9 factorial is 362,880 in the numerator, and 3! 4! and 5! multiplied

together in the denominator equal 288.

P = 9! / 3! *4! *2!

= 9*8*7*6*5*4*3*2*1/3*2*1*4*3*2*1*2*1.

Simplify the fraction by dividing.

There are 1,260 ways to arrange the nine family members by shirt color.

Example: A family goes to a studio to have their photo taken, and the photographer must arrange them to get the best shot. Three of them are male and five of them are female. How many ways can the photographer arrange the family members?

In this example, there are a total of 8 family members regardless of gender, so the n

value is 8. Either group of identical objects can be substituted as the x value because

the denominator comes out the same no matter what. Notice that, whatever the case,

the sum of the numbers in the denominator (5 and 3) is always equal to the number

If men are the x value:

P= 8! / (8! -3!)3!

=8! /5! *3!

If women are the x value:

P=8! / (8-5)! *5!

= 8! /3! *5!

In the numerator, 8! equals 40,320 while in the denominator 3! multiplied by 5!

equals 720.

P=8! /5! *3! = 8*7*6*5*4*3*2*1 / 5*4*3*2*1

= 40320/720

= 56

There are 56 ways the photographer can arrange 3 men and 5 women.

Read complete chapter click Maths NCERT Solutions Class 11 - Permutation

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