4.4 Problems 1. Evaluate: (a) P(8,6) (b) P(4,2) (c) P(9,5) (d) P(10,2) (e) P(5,5

Question

4.4 Problems 1. Evaluate: (a) P(8,6) (b) P(4,2) (c) P(9,5) (d) P(10,2) (e) P(5,5) (f) P(26,3) 2. Show that n(n-1)! 3. Show that n! = n(n-1) (n-2)! 4. How many permutations of A,B,C,D,E are there? 5. How many permutations of 3 of the 5 letters A,B,C,D,E are there? 6. How many different permutations of A A A A B? 7. How many different permutations are there of 8 letters 5 of which are H's and 3 of which are T's? 8. If a coin is tossed 5 times find the probability of getting 3 heads and 2 tails. List the sample space and check.

Explanation / Answer

5)

here as we need to select 3 out of 5 letter and then arrange them in order ; number of permutations

=5P3 =5!/(5-3)! =120/2 =60

6)

as there are 4 A's and 1 B out of 5 letter ; number of arrangement =5!/(4!*1!) =120/24 =5

(Note : we can see that intuitively also that B can take any of 5 places in or out of A's; threfore there are 5 ways to arrange them)

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