Question 146040: Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
a.) the first letter must be Y
b.) the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first).
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use either the fundamental counting principle or the permutation formulas (or both) to answer the following:
Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
a.) the first letter must be Y
1st letter --- 1 way
next 4 letters: 4!= 24 ways
Total: 1*24 = 24
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b.) the vowels and consonants alternate, beginning with a consonant (Y is a consonant here and Y does not have to be first).
# of vowels: 2
# of consonents: 3
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1st letter(consonent): 3 ways
2nd letter(vowel): 2 ways
3rd letter(consonent): 2 ways
4th letter(vowel): 1 way
5th letter(consonent: 1 way
Total: 3*2*2*1*1 = 12
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Cheers,
Stan H.
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