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How many different words of 3 length can be formed from a,e,i,o,u containing a,e ?
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There are 3 places to put a character at first place we can put 5 character same as second and third places (7 character out of which 5 are distinct) hence 5*5*5 =125.,( With repeat)
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For without repetation, as we must include a and E only one place will be left, a and E can be arranged in 3 places in 3 p 2 ways, we have three letters now so 3 p 2 * 3 = 18

Don't take 3 c 2, as we are doing arrangements not selectetion so order matters.

For repetation allowed

We can arrange a and E in 3 p 2 ways, one place is left, we have 5 letters so it will be 3 p 2 * 5 = 30

when you are taking ae and filling the third place with a,e also ,then there will be 6 strings double counted. So answer will be 24. ( 30 - 6)
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