# Math Help - Number of Choices..

1. ## Number of Choices..

Hi all,

Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
a) Exactly 3 consonants
b) No vowels
c) At least one vowel

2. Originally Posted by cu4mail
Hi all,

Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
a) Exactly 3 consonants
b) No vowels
c) At least one vowel
${10}\choose{5}$

3. ## Thanks

Originally Posted by colby2152
${10}\choose{5}$
Thanks for help.

4. Originally Posted by cu4mail
Hi all,

Five different letters are chosen from A,B,C,D,E,F,G,H,I & J.Find the number of choices. How many of these choices contain
a) Exactly 3 consonants
b) No vowels
c) At least one vowel
I think I can answer, if anyone wants to check my work I wouldn't mind

a) 3 of your letters are used up by choosing vowels. So you have 2 choices left out of 7: (10-3)C(5-3) = 7C2 = 21

b) You still need to select 5 letters, but your set is smaller (10-3)C5 = 7C5 = 21

c) This should be the set of all choices minus the set of no vowels. 10C5 - 7C5 = 252 - 21 = 231

I am moderately confident in my answers, but I haven't looked at these in a while, so take it with skepticism.

edit: I think I did a wrong, I calculated how many vowels instead of how many consonants.