Posted by Soroban on September 21, 2002 at 18:20:50:
In Reply to: consecutive numbers posted by oldguy on September 21, 2002 at 15:25:26:
: I meant any consecutive order i.e. 1 5 21 23 25. 6 11 13 24 25. ect.
You meant "increasing order" - which is irrelevant. Since the
25 numbers are distinct, we can always PUT them in increasing order.
"Consecutive" has a very precise meaning in number problems.
I believe the answer is 25C5 = 25!/5!20! = 53,130.
Before the Math Police breaks down my door, let me explain.
There are 25 cards, numbered 1 to 25. You are to select 5 of them.
AFTER you have selected them, you can THEN arrange them in order.
If you happen to select {7,24,3,19,8} in that order, you still have
one possible set: {3,7,8,19,24}, right?