Question

How many bit strings of length 10 contain exactly six 1s?

Answer 1

Using combination

`\\ \sf\longmapsto {}^(10)C_6`

We know

`\boxed{\sf {}^nC_r=(n!)/(r!(n-r)!)}`

`\\ \sf\longmapsto (10!)/(6!(10-6)!)`

`\\ \sf\longmapsto (10!)/(6!(4!))`

`\\ \sf\longmapsto 210`

Answer 2

9514 1404 393

Answer:

210

Explanation:

The number of combinations of 10 things taken 6 at a time is ...

10!/(6!(10-6)!) = 210

210 bit strings of length 10 will have 6 1-bits.