SOLUTION: 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,begin

Question 358137: 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 consonanthere and Y does not have to be first)
Please help im lost with this question i would appreciate it
Found 3 solutions by jrfrunner, Edwin McCravy, sudhanshu_kmr:
Answer by jrfrunner(365)   (Show Source): You can put this solution on YOUR website!
a) The first letter must be Y
Since there only 4 letters free to be chosen, the answer = 4!=24
==
b) The vowels and consonants alternate,beginning with a consonant
-
let C=consonant, V=vowel
There are 3 C and 2 V
CVCVC
Number of ways 3*2*2*1*1=12

Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
Using the letters of the word YOUNG, tell how many different 5-letter combinations are possible if:
a) The first letter must be Y

Y _ _ _ _ There is 1 way to choose the 1st letter, since it must be a Y. There are 4 letters left to choose for the 2nd letter. There will then be 3 letters left to choose for the 3rd letter. There will then be 2 letters left to choose for the 4th letter. There will then be only 1 letter left to choose the for 5th letter. Answer 1*4*3*2*1 = 24. Checking: 1. YOUNG 2. YOUGN 3. YONUG 4. YONGU 5. YOGUN 6. YOGNU 7. YUONG 8. YUOGN 9. YUNOG 10. YUNGO 11. YUGON 12. YUGNO 13. YNOUG 14. YNOGU 15. YNUOG 16. YNUGO 17. YNGOU 18. YNGUO 19. YGOUN 20. YGONU 21. YGUON 22. YGUNO 23. YGNOU 24. YGNUO

b) The vowels and consonants alternate,beginning with a consonant (Y is a consonant there and Y does not have to be first)

They can only alternate this way: consonate, vowel, consonant, vowel, consonant There are 3 consonants to choose for the 1st letter. There are 2 vowels to choose for the 2nd letter. There will then be 2 consonants left to choose for the 3rd letter. There will then be only 1 vowel left to choose for the 4th letter. There will then be only 1 consonant left to choose for the 5th letter. That's 3*2*2*1*1 = 12 ways Checking: 1. YONUG 2. YUNOG 3. YOGUN 4. YUGON 5. NOYUG 6. NUYOG 7. NOGUY 8. NUGOY 9. GONUY 10. GUNOY 11. GOYUN 12. GUYON Edwin

Answer by sudhanshu_kmr(1152)   (Show Source): You can put this solution on YOUR website!

Here 3 consonants and 2 vowels.
A) no. of words where first letter is y = 4P4 = 4! = 24
( no. of ways to arrange 4 letters O,U,N and G on four places i.e YXXXX )

............................................................................
B)
now, words must be in format CVCVC

where c- consonants, v -vowels
For first place we can put either N or G, because Y can't be on first place.
no. of ways = 2

For second place we can put either O or U. so, no. of ways = 2
similarly, for third place, no. of ways = 2 ( Y or remaining of N , G )
For fourth place , no. of ways = 1 (only one vowel left)
For fifth place, no. of ways = 1 (only one consonants left)

so, no. of words = 2* 2 * 2 * 1 * 1 = 8

Sometimes there may be typing mistake in solution of a problem, so please ignore it. Understand the concept and try to solve the problem yourself. If there is problem related to concept, contact at
sudhanshu.cochin@yahoo.com or sudhanshu.cochin@gmail.com
Best of luck.......
RELATED QUESTIONS
Use either the fundamental counting principle or the permutation formulas (or both) to... (answered by Electrified_Levi)
Use either the fundamental counting principle or the permutation formulas (or both) to... (answered by stanbon)
Using the letters of the word YOUNG, tell how many different 5-letter combinations are... (answered by jim_thompson5910)
1.In how many different ways can 6 classes be scheduled during a 6-period day? 2.In how... (answered by stanbon)
Radio station call letters consist of four upper case letters. If the first letter must... (answered by TimothyLamb)
How many four-letter combinations of the letters of the word EQUATION contain letter Q? (answered by ikleyn,greenestamps)
How many three-letter combinations are possible using the letters D,E,F,G and... (answered by Alan3354)
a) Using the letters in the word "OCTAGON," how many distinct arrangements using all 7... (answered by stanbon)
if 4-letter "words" are formed using the letters A, B, C,D,E, F,G, how many such words... (answered by sudhanshu_kmr,edjones)