Class 11

Math

Co-ordinate Geometry

Straight Lines

In a crossword puzzle, $20$ words are to be guessed of which $8$ words have each an alternative solution also. The number of possible solutions will be

- $_{20}P_{8}$
- $_{20}C_{8}$
- $512$
- $256$

So $12$ words are fixed, so they won't affect the number of ways.

So now we find the number of ways in which the remaining $8$ words can be guessed.

Now every word have $2$ solutions,

so there are $2$ ways to fill each of these words, and for $8$ such words,

it can be done in $2×2×2×2×2×2×2×2=2_{8}=256$ ways.