• Dec 28th 2008, 02:46 PM
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?

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?

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
• Dec 28th 2008, 04:51 PM
Mush
Quote:

Originally Posted by 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?

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?

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

Yes, all very good. Apart from in c), I'd just like to point out that probability of an event is usually expressed as a number between 0 and 1. Not a percentage.
• Dec 28th 2008, 09:27 PM
mr fantastic
Quote:

Originally Posted by 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?

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?