There are five vowels. Notice that any of the vowels could be chosen from 0 though 5 times in any given combination. We therefore need the number of combinations of 5 from 5 _with replacement_.
This is the number ( 5 + 5 - 1 ) choose 5 = 126.
There are 3 consonants from 21 and 2 vowels from 5. That gives 21C3 * 5C2 combinations = 21*20*19/(3*2*1) *5*4/(2*1) = 1330*10 = 13300 combinations in all.
Two make combinations you would take 2x1=2 combinations only
27^27
6
From 4 letters, you can create three-letter combinations by selecting any 3 letters from the 4 and arranging them. The number of ways to choose 3 letters from 4 is given by the combination formula ( \binom{4}{3} = 4 ). Each of these combinations can be arranged in ( 3! = 6 ) ways. Therefore, the total number of three-letter combinations is ( 4 \times 6 = 24 ).
There are 3 consonants from 21 and 2 vowels from 5. That gives 21C3 * 5C2 combinations = 21*20*19/(3*2*1) *5*4/(2*1) = 1330*10 = 13300 combinations in all.
That is a trick question. You can't make a four letter word using all five vowels.
The other combinations you can make using that letter combination are:lightlightssighsight
1
The word "your" has one vowel, which is the letter 'o'.
5 x 21 = 105
3,124,550 possible combinations
21^4
There are many five letter words with no vowels. Crypt, Cysts, Dryly, Flyby, Glyph and Gypsy are some examples. If you don't consider Y a vowel!
Two make combinations you would take 2x1=2 combinations only
27^27
You did not give us the set to work with...