Question

In how many ways can 5 colours be selected out of 9

Answer 1

See the attach file for ur ans

Answer 2

There are total 126 ways, to select 5 colours from 9.

Step-by-step explanation:

Given:

• 9 colours.

To find:

• In how many ways can 5 colours be selected out of 9?

Solution:

Concept/Formula to be used:

If 'r' items to be selected from 'n' items, then

Number of ways to select

$\bf ^{n} C_r = \frac{n!}{r!(n - r)!}$

Step 1:

Write the values of n and r.

As, there are total 9 colours, so n=9

selection of 5 colours to be made, r=5

Number of ways=$\bf ^{9} C_5$

Step 2:

Find number of ways.

$^{9} C_5= \frac{9!}{5!4!}$

or

$= \frac{9 \times 8 \times 7 \times 6 \times 5!}{5! \times 4 \times 3 \times 2 \times 1}$

or

$= 9 \times 2 \times 7$

or

$= 18 \times 7$

or

$= 126$

Thus,

There are total 126 ways, to select 5 colours from 9.

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