Question

Question #22c63

Answer 1

`color(white)('x")^11P_n = 11 * 10 * 9` `color(white)("XX")rArrcolor(white)("XX")n=3`
but `color(white)("x)^nP_(11) = 11 * 10 * 9` has no solution for `n`

Explanation:

`color(white)("x")^aP_b = (a!)/((a-b)!)`

`color(white)("x")^11P_n = (11!)/((11-n)!)`

`color(white)("XX")=(11 * 10 * 9 * 8 * 7 * ... * 1)/((11-n) * (10 -n) * ... * (1))`

`11 * 10 * 9 = (11 * 10 * 9 * cancel(8) * cancel(7) * ... * cancel(1)1)/(cancel((11-3)) * cancel((10 -3)) * ... * cancel((1)))`

`rArr n=3`