E(4) into E(6)

Probability Level 3

How many different injections are there from E ( 4 ) = { 1 , 2 , 3 , 4 } E(4) = \{1, 2, 3, 4\} into E ( 6 ) = { 1 , 2 , . . . , 6 } E(6) = \{1, 2, . . . ,6\} ?


The answer is 360.

Kees Vugs by Kees Vugs , 87, Netherlands

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Choose 4 elements from E(6) by 6C4 and then just permutation among them by 4! . So total ways is (6C4).4! = 15x24 = 360

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Kees Vugs
Aug 11, 2018

Let i(n, m) be the number of injections from {1, 2, . . ., n} into {1, 2, . . ., m}. Clearly i(n, m) = 0 when m < n and i(n, m) = n! when m = n.If m > n then 1 in E(n) has m possible images, 2 in E(n) has still (m - 1) possible images . . . n in E(n) has still (m - (n - 1)) possible images. Total number of possibilities is m x (m - 1) x . . . x (m - n + 1) or \frac {m!}{(m - n)!}. And in this case \frac {6!}{2!} = 360.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...