Question

how many 5-letter arrangements of the letters R E G I O N A L consisting of 3 consonants and 2 vowels can be formed if no letter is repeated?

Answer 1

How many consonants and vowels are there?

Answer 2

4 consonants and 4 vowels

Answer 3

In how many ways you can arrange 2 vowels out of 4?

In how many ways you can arrange 3 consonant out of 4?

Answer 4

so 4C2 * 4C3?

Answer 5

well first you select first 2 vowels from 4 so thats:
4!/2!2!
then you select 3 consonants from 4:
4!/2!2!+4!/3!1!
and then we arrange them so thats just 5! because for the first letter word, we have 5 choices, for 2nd, since rep. not allowed 4 choices, for 3rd, 3 choices, 4th, 2 choices, 5th one choice, 1. So we'll have
4C2+4C3+5!

Answer 6

I don't get how you got the 5 factorial and why are you adding these?

Answer 7

288 is the answer?

Answer 8

I don't know I'm still not sure about this :(

Answer 9

I think it is (number of vowel combinations)* (number of consonant combinations)*(number of 5 letter arrangements), so 4C2*4C3*5! should be correct

Answer 10

I don't get it, am I supposed to add or subtract?

Answer 11

you shoud multiply, combinations work that way: for example
(5 combinations)*(3 combinations)=(c1+c2+c+c4+c5)*(comb1+comb2+comb3)= 15 diferent options

Answer 12

thank you!