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Home » How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
CBSE | Class 11 | Combinations | Exercise 17.2 | Maths | RD Sharma
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?

Given:

Total boys are

    \[=\text{ }25\]

Total girls are

    \[=\text{ }10\]

Boat party of

    \[8\]

to be made from

    \[25\]

boys and

    \[10\]

girls, by selecting

    \[5\text{ }boys\text{ }and\text{ }3\text{ }girls\]

So,

By using the formula,

    \[^{n}{{C}_{r}}~=\text{ }n!/r!\left( n\text{ }-\text{ }r \right)!\]

    \[^{25}{{C}_{5}}~\times {{~}^{10}}{{C}_{3}}~=\text{ }25!/5!\left( 25-5\right)!\times 10!/3!\left( 10-3 \right)!\]

Or,

    \[=\text{ }25!\text{ }/\text{ }\left( 5!\text{ }20! \right)\text{ }\times \text{ }10!/\left( 3!\text{ }7! \right)\]

    \[=\text{ }\left[ 25\times 24\times 23\times 22\times 21\times 20! \right]/\]

    \[\left( 5!\text{ }20! \right)\text{ }\times \]

    \[~\left[ 10\times 9\times 8\times 7! \right]/\left( 7!\text{ }3! \right)\]

Or,

    \[=\text{ }\left[ 25\times 24\times 23\times 22\times 21 \right]/5!\text{ }\times \text{ }\left[ 10\times 9\times 8 \right]/\left( 3! \right)\]

Or,

    \[=\text{ }\left[ 25\times 24\times 23\times 22\times 21 \right]/\]

    \[\left( 5\times 4\times 3\times 2\times 1 \right)\text{ }\times \]

    \[\left[ 10\times 9\times 8 \right]/\left( 3\times 2\times 1 \right)\]

Or,

    \[=\text{ }5\times 2\times 23\times 11\times 21\text{ }\times \text{ }5\times 3\times 8\]

    \[=\text{ }53130\text{ }\times \text{ }120\]

So,

    \[=\text{ }6375600\]

∴ The total number of different boat parties is

    \[6375600\]

ways.

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