1.) How many three- letter \"words\" are possible that include the letter \'m\'

Question

1.) How many three- letter "words" are possible that include the letter 'm' at least once? Note that any string of letter constitutes a "word".

2.) Mr. Fish purchases a baker's dozen of bagels. 5 of the bagels are plain, 3 are garlic, 3 are poppy seed, and 2 are onion. When Mr. FIsh gets to his office, he randomly takes out 4 bagels to bring home for his family. a.) How many possible ways is it possible for Mr. Fish to choose exactly one of each type of bagel? b.) How many possible ways is it possible for Mr. Fish to choose at lleast one garlic bagel?

3.) A coin is tossed 9 times. a.) How many different outcomes are possible? b.) How many outcome have exactly 5 heads? c.) How many outcomes have at least 2 heads?

Explanation / Answer

As per the Chegg policy, we are advised to do one question at a time so i am attempting the 1st one.

1. Total number of three letter words possible = 26*26*26 = 17576

Now,

Number of three letter words without any "m" = 25*25*25 = 15625

Hence,

Number of three letter words with atleast one m

= Total number of words - Number of three letter words without any "m"

= 17576 - 15625

= 1951

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