Permutation of n taken r at a time expressed as P(n,r) has
the formula
P(n,r) = [tex] \frac{n!}{(n-r)!} [/tex]
P(120, 3) = [tex] \frac{120!}{(120-3)!} [/tex] = [tex] \frac{120!}{117!} [/tex]
By factorial definition,
120! = 120x119x118x117x116x...x3x2x1
117! = 117x116x...x3x2x1
So,
[tex] \frac{120!}{117!} [/tex] = [tex] \frac{120x119x118x117!}{117!} [/tex] (Note that [tex] \frac{117!}{117!} = 1[/tex])
[tex]= \frac{120x119x118x117!}{117!} [/tex]
=[tex]=120x119x118[/tex]
=1685040
Therefore, the first, second, and third prizes can be drawn in 1,685,040 ways.
