Question

Find the number of distinct five letter arrangements that can be made from
two identical vowels and three Bs​

Answer 1

Step-by-step explanation:

So you need to count:

(1)Arrangements of the vowels and consonants.

(2)And multiply by 21 (unique consonants) and then by 5 (unique vowels)

(1)The arrangements of the vowels is 5-choose-2 - you are picking two spots for vowels from five available. That fixes the consonants in the other three spots.

Note that is the same as 5-choose-3, which makes sense as you could have picked the spots for the consonants instead, fixing the vowels in the two left over spaces.

5C2 is 5*4/2 =10

{VVCCC,VCVCC,VCCVC,VCCCV,CVVCC,CVCVC,CVCCV,CCVVC,CCVCV,CCCVV} listed here.

(2)V can be any of 5, C any of 21.

So the total distinct “words” is 10*21*5=1050