Find the number of permutations of 8 things taken 5 at a time.

Solution:

We have permutation of ‘n’ things taken ‘r’ at a time is 

\(_{}^{n}\textrm{P}_{r} = \frac{n!}{(n - r)!}\)

Here n = 8 and r = 5 

_{}^{8}\textrm{P}_{5} = \frac{8!}{(8 - 5)!} = \frac{8\times 7\times 6\times 5\times 4\times3\times 2\times 1 }{3\times 2\times 1}= 6720\)

The above arrangement will include only those cases where repetition is not allowed

If repetition is allowed then the permutation of ‘n’ things taken ‘r’ at a time is \(n_{}^{r}\)

Then the number of permutation possible = 8⁵ =32768

Find the number of permutations of 8 things taken 5 at a time.

Find the number of permutations of 8 things taken 5 at a time.

Summary:

Permutations of 8 things taken 5 at a time (i) When the repetition not allowed = 1680, (ii) When repetition allowed = 8⁵ = 32768