Question

Suppose we want to choose 6 letters , without replacement , from 8 distinct letters

Answer 1

Answer:

$Total\ number\ of\ ways=20160$

Step-by-step explanation:

$Number\ of\ ways\ to\ choose\ first\ letter=8\\\\Number\ of\ ways\ to\ choose\ second\ letter=7\\\\Number\ of\ ways\ to\ choose\ third\ letter=6\\\\Number\ of\ ways\ to\ choose\ fourth\ letter=5\\\\Number\ of\ ways\ to\ choose\ fifth\ letter=4\\\\Number\ of\ ways\ to\ choose\ sixth\ letter=3\\\\Total\ number\ of\ ways=8\times 7\times 6\times 5\times 4\times 3\\\\Total\ number\ of\ ways=20160$

Other Method:

Since letters are taken without replacement, that means order of selection matters. we have to take permutation here.

$Total\ number\ of\ ways=^6P_2\\\\Total\ number\ of\ ways=\frac{8!}{(8-6)!}\\\\Total\ number\ of\ ways=\frac{8!}{2!}\\\\Total\ number\ of\ ways=20160$