Question

30)A pianist plans to play 6 pieces at a recital from her repertoire of 27 pieces, and is carefully considering which song to play first, second, etc. to create a good flow. How many different recital programs are possible?
31)Suppose a designer has a palette of 9 colors to work with, and wants to design a flag with 2 vertical stripes, all of different colors.

How many possible flags can be created?

32)From a group of 8 people, you randomly select 5 of them.

What is the probability that they are the 5 oldest people in the group?

Give your answer as a fraction

33)You pick 6 digits (0-9) at random without replacement, and write them in the order picked.

What is the probability that you have written the first 6 digits of your phone number? Assume there are no repeats of digits in your phone number.

Give your answer as a fraction.

36)A girl has 7 skirts, 10 blouses, and 4 pairs of shoes. How many different skirt-blouse-shoe outfits can she wear? (Assume that each item matches all the others, so she is willing to wear any combination.)
Your answer is

37)Standard automobile license plates in a country display 2 numbers, followed by 2 letters, followed by 3 numbers. How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)
Your answer is

38)A true-false test contains 21 questions. In how many different ways can this test be completed. (Assume we don't care about our scores.)
Your answer is

39)How many three-letter "words" can be made from 9 letters "FGHIJKLMN" if repetition of letters
(a) is allowed?
Your answer is :   
(b) is not allowed?
Your answer is

40)In how many ways can first, second, and third prizes be awarded in a contest with 245 contestants?
Your answer is


41)Find the number of distinguishable permutations of the given letters "AAABBBCC".
Your answer is

Answer 1