Question

Part 1.
Suppose you have a cookie jar that contains 13 chocolate chip cookies and 33 oatmeal cookies. If you reach in the jar and pull out 2 cookies at random, find the probability that both are chocolate chip. Express answer to two decimal places.

Part 2.

You decide it would be fun to go to a magic show. The magician picks you out of the crowd and writes down 3 digits (0-9) at random without replacement. He writes them in the order picked.

What is the probability that he has written the first 3 digits of your address? Assume there are no repeats of digits in your address.

Give your answer as a fraction.

Part 3.
Find the number of distinguishable permutations of the given letters "XXXYYZ".

Answer 1

1) probability that both are chocolate chip =(13/46)*(12/45)=0.08

2)

total number of ways of arrangement of 3 digits =10*9*8 =720

therefore probability =1/720 (Note:this should be 6/720 =1/120 if order of your address digit does not matter)

3)

there are 3 X, 2 Y and 1 Z

hence number of permutations =6!/(3!*2!*1!) =60