Number of words of 4 letters that can be formed with the letter of the word IITJEE is...............

the answer is 468

102

Approved

answer is 256

Ans. Is 14!!!

» four distinct letters= (4C4)

»Of form (aabb)= (2C1).(4C2)

»Of form aabc= (2C2)

So 0n adding it comes 14.

is that 6*6*6*6=1296? is that the answer?

72

there will be following cases

1) words form by letters I,T,J,E

we will use permutation

4! =24

2) words form by only I,I,E,E

there would be following arrangement

IIEE   another word by flipping the letters I,E

IEEI another word by flipping the letters

EIEI  another word by flipping the letters

it makes total of 6

3) words formed by 2 I''S T,J,E

first select 2 places out of four so we use combination

3C2  and then arrange 3 letters in 2 places

so finally we get

4C2*6 = 36

4) words formed by 2 E''S  AND T,J,E

so again 36

so add all cases you will get the answer

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184

IITJEE Can be written as " II ", "T" , "J" , "EE" here there are two sets of repeated combinations(I,J) .now the four letter words can be categorised into (i)two similar,another two similar 2C1*(4!/(2!*2!)) ways. (ii)two similar , 1 different , another different 2C1*(3C2)*(4!/2!) ways (iii)All different 4! ways so the total number of 4 letter words= 12+72+24=108

90

there will be following cases 1) words form by letters I,T,J,E we will use permutation 4! =24 2) words form by only I,I,E,E there would be following arrangement IIEE another word by flipping the letters I,E IEEI another word by flipping the letters EIEI another word by flipping the letters it makes total of 6 3) words formed by 2 I``S T,J,E first select 2 places out of four so we use combination 3C2 and then arrange 3 letters in 2 places so finally we get 4C2*6 = 36 4) words formed by 2 E``S AND T,J,E so again 36 so add all cases you will get the answer

24

no restriction means digits can be repeated if first place is filled by I then possible arrangements are 5!/2! if first place is filled by T then possible arrangements are 5!/(2!*2!) if first place is filled by J then possible arrangements are 5!/(2!*2!) if first place is filled by E then possible arrangements are 5!/2! total no of arrangements are 60+30+30+60=180