Using the standard 26-letter alphabet, how many different groups of 4

I am not sure what i am doing wrong.
5 ways to choose a vowel. 2 vowels allowed -> 5*5 = 25
21 ways to choose a consonant. y cannot be chosen. 20 ways to choose. 2 consonants allowed -> 20*20.

Brining it all together -> 5*5*20*20 = 10,000

mehrotrayashraj your are conisdering "ae and ea" to be different.. the question stem say, different groups,, in group of "a,e, p,m" is same as "e,a,p,m".

in short u have used permutations,, which is not required here

I think you mean 5c2

phew! be to that typo yar but rest of the calculation was correct.Any way i do stand corrected

Using the standard 26-letter alphabet, how many different groups of 4 letters are possible, if exactly two letters are chosen from a, e, i, o ,u and two letters are chosen from all the remaing letters except for y, and a letter can be used more than once?

A. 500
B. 1900
C. 2500
D. 3150
E. 6300

Note -As it says group assuming that the arrangement doesn't matter

group with both repetitive consonants and vowels = 4C1*20C1 = 80
group with repetitive consonants and non repetitive vowels = 20C1* 5C2 = 200
group with repetitive vowels and non repetitive consonants = 21C2* 4C1 = 840
group with both non repetitive consonants and vowels = 21C2*5C2 = 2100
total = 3220
Can anyone pls tell me where I went wrong

sreenu7464 Please see the highlighted areas

Hi, I can't get the reason for 2 vowels we use 5C2 + 5C1 = 10 + 5 = 15. I think even if a could not be repeated we would use 5C2*2! or in other words 5х4 (5 options for the first letter and 4 options for the second letter in the word).

Why are we adding 5C2 and 5C1... Doesn't 5C2 mean a combination of two letters from 5 total options?

Hi everyone, can someone help me to explain why it's 20C2? I thought it's supposed to be 23C2 (as y and a can be used more than once so only e, o, u are not counted).

Thank you so much

Did anyone else think that the question is saying that only one of the letters could be repeated? It seems that the answer is saying both letters from a,e,i,o,u and the remaining letters except y can both be repeated.

Hi! Why have you taken "20" C2? there are 26 letters in total to choose from?

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