1 How many permutations are there of the set u v w x y z 2

1) How many permutations are there of the set {u, v, w, x, y, z} ?\\

2) In how many different orders can 6 runners finish a race if no ties areallowed?

3) How many subsets with an even number of elements does a set with 9 elements have?

Solution

Answer:

There are 6 elements in the set : { u , v , w , x, y , z }

Now there are 6 posibilitties for u , v 5 , w 3 and so on ...therefore permutations possible = 6 * 5*4*3*2*1 = 1944

2. P( 6,6 ) = 6! = 720

3. We know that (1+x)^n + (1-x)^n

put x = 1 , we get

(1+1)^n = 2^n/2 , n = 9 , therefore it becomes 2^9/2 = 2^8