Question

In How many ways 4 toys can be selected from 8 toys. ​

Answer 1

The number of ways to select 4 toys out of 8 is 1680 if selected toys are excluded and 4096 if they are included.

We have to find the number of ways to select 4 toys from 8 toys.

condition 1 : When selected toys are excluded

• We have given 8 toys and have to select 4 toys from these 8 toys.
• Let's assume we have four boxes ; that is A , B , C and D and each box can contain one toy.
• first box, A can select a toy from all 8 toys so the number of ways to select a toy to the box A is 8.
• 2nd box , B can select a toy from (8 - 1) toys so the number of ways to select a toys to the box B is 7
• similarly 3rd box , C and 4th box D can select their toys 6 and 5 ways respectively.
• So, the total number of ways to select 4 toys for four boxes is 8 × 7 × 6 × 5 ways

Therefore the number of ways to select 4 toys out of 8 is 8 × 7 × 6 × 5 = 1680 ways.

condition 2 : when selected toys are included.

• It is the easiest condition to solve it. we can select in 8 ways.
• So, the total number of ways to select four toys put of 8 toys is 8 × 8 × 8 × 8 ways

hence, the number of ways = 8 × 8 × 8 × 8 = 8⁴ = 4096 ways.

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