<PRE><B>Question 1030226</B>
P(n,r) = nPr = n! / (n-r)!
:
********************************************************************
1) P(7,r) = 7Pr = 7! / (7-r)!
:
60 * P(7, r-3) = 7! / (10-r)!
:
7! / (7-r)! = 60 * 7! / (10-r)!
:
1 / (7-r)! = 60 / (10-r)!
:
cross multiply fractions
:
(10-r)! = 60 * (7-r)!
:
(10-r)(9-r)(8-r)(7-r)(6-r) * ... = 60 * (7-r)* (6-r) * (5-r) * ...
:
(10-r)(9-r)(8-r) = 60
:
r can be at most 7, trial and error finds r = 5
********************************************************************
2 and 3 use the same method
:</PRE>