How many different arrangements can be made by taking 3 letters of the

120 is correct.

6P3 = 6!/3! = 6X5X4 = 120.

I've a doubt and maybe it's not a good question. Why are we using combination here. As I was reading in case of arrangement, we always use permutations. Thanks

Asked: How many different arrangements can be made by taking 3 letters of the word SUNDAY ?

6C3×3! = 20×6 = 120

IMO E

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Hi Bhavika01. First of all no question is unimportant.

The usage of combinations is just another thought process. When choices come in along with arrangements, I find it much easier to use combinations as long as we do not forget to arrange what is chosen.

Also in terms of calculations, nCr * r! = nPr, so there isn't any hard and fast rule that in an arrangements question, nPr has to be used.

For eg how many words can be formed with A, B, C D, E where the 1st and last have to be consonants.

You can either do it as 3P2 * 3! where you are arranging 2 of the 3 consonants and then arranging the remaining 3 or you can do it as 3C2 * 2! * 3!
where you choose 2 consonants for the 2 places, arrange them in 2! ways and then the remaining 3 is arranged in 3! ways.


My suggestion is go by the approach which is most comfortable. You can dabble with different methods once you get the basic understanding.


Hope this helps.


Arun Kumar

Arrangement when the order matters and there’s no repetition.