Question

There are 5 boys and 3 girls. In how many ways can they stand in a row.
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Answer 1

Question :-

There are 5 boys and 3 girls. In how many ways can they stand in a row ?

Answer :-

CASE 1 : when girls and boys can stand between each other in a row

Thus,

No. of WAYS

= ( no. of boys + no. of girls )!

= ( 5 + 3 )!

= 8!

= 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

= 40,320 ways

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CASE 2 : when not even a single girl/boy can stand between two boys/girls respectively

Thus,

No. of WAYS

= ( no. of boys )! × ( no. of girls )!

= 5! × 3!

= 120 × 6

= 720 ways

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More Information :_

Kɴᴏᴡʟᴇᴅɢᴇ ᴏғ Fᴀᴄᴛᴏʀɪᴀʟ

The symbol of factorial is an exclamation mark "❗".

For example, n! = n × (n-1) × (n-2) × (n-3) × … × 3 × 2 × 1

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