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**cnmath16** 46. a) How many five-letter "words" (combinations of letters) can be formed from the word "March"?

Answer: 5! = 5 x 4 x 3 x 2 x 1

= 120 different words can be formed

b) In how many of these words are M and R together?

Answer:

0 letters in front = 2 x 1 x 3 x 2 x 1 = 12

1 letter in front = 3 x 1 x 1 x 2 x 1 = 12

2 letters in front = 3 x 2 x 2 x 1 x 1 = 12

3 letters in front = 3 x 2 x 1 x 2 x 1 = 12

Therefore there are 48 words where M and R will be together.

c) What is the probability of M and R not occurring together?

Answer:

48/120 = x/100

= 40% probability that they will be together

Therefore, there is a 60% probability that M and R won't be together