`A,B,C,D` develop `18` items. Five items jointly by `A` and `C`, four items by `A` and `D`, four items by `B` and `C` and five items by `B` and `D`. The number of ways of selecting eight ites out of `18` so that the selected ones belong equally to `A,B,C,D` is

Options

A. `5226`
B. `5626`
C. `4418`
D. `4936`

Answer

B

Explanation

`(b)`
Required number of ways of selecting `8` times out of `'18'` so that selected ones belong equally to `A`, `B`, `C`, `D`
`=(.^(5)C_(2))^(2)*(.^(4)C_(2))^(2)+(.^(5)C_(1))^(2)*(.^(4)C_(3))^(2)+(.^(5)C_(3))^(2)*(.^(4)C_(1))^(2)+(.^(5)C_(4))^(2)+(.^(4)C_(4))^(2)`
`=100xx36+25xx16+100xx16+25+1`
`5626`