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