- #1

Euler2718

- 90

- 3

## Homework Statement

[tex] \dbinom{7}{r} = 21 [/tex]

## Homework Equations

[tex] \dbinom{n}{r} = \frac{n!}{(n-r)!r!} [/tex]

## The Attempt at a Solution

[tex] \dbinom{7}{r} = 21 [/tex]

[tex] \frac{7!}{(7-r)!r!} = 21 [/tex]

[tex] 7! = 21(7-r)!r! [/tex]

[tex] 240 = (7-r)!r! [/tex]

So I get here and the convention is to guess in check (to my knowledge). I found a way to do it on my TI-84; simply go y= 7 nCr x ; then observe the table to gather the solutions of 5 and 2. But how would you do this algebraically (no guess and check)?