If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in

Total ways of arrangement can be explained by the following steps

- - - - -
5 blank spaces to be filled by each of 5 digits

First Place can be filled in 5 ways (any digit out of available 5 digits)
Second Place can be filled in 4 ways (any digit out of Remaining available 4 digits because one digit has been used already)
Third Place can be filled in 3 ways (any digit out of Remaining available 3 digits because Two digits have been used already)
Forth Place can be filled in 2 ways (any digit out of Remaining available 2 digits because Three digits have been used already)
Fifth Place can be filled in 1 ways (any digit out of Remaining available 1 digits because Four digits have been used already)

Total Arrangements = 5 x 4 x 3 x 2 x 1 = 5! = 120

Answer: Option E

A = {1,2,3,4,5}

Let X1-X2-X3-X4-X5 be the slot to be filled.

X1 slot can be filled by any of the 5 elements of A in 5 ways.
X2 slot can be filled by any of the 4 elements of A in 4 ways.
X3 slot can be filled by any of the 3 elements of A in 3 ways.
X4 slot can be filled by any of the 2 elements of A in 2 ways.
X5 slot can be filled by any of the 5 elements of A in 1 way.

Therefore, 5 digits can be arranged in 5*4*3*2*1 = 120 ways. Ans (E).

This is combinations without repetition, single source and order does matter. Btw. most questions in GMAT however involve combinations where order doesn't matter.

Here it's simply 5! = 120

You should know the value of 5! by heart.

If a number is only used once, the total number of digits available is reduced by one each time.

5*4*3*2*1 = 5! = 120

800score Official Solution:

There are 5! = 120 possible arrangements of the five digits with no restrictions. Every time an item is selected, it is reduced from the pool. (5)(4)(3)(2)(1) = 120.

In how many ways can the 5 digits be arranged if then numbers in the set A could be used more than once ?

In that case, then you could take the same approach, but you would not reduce the available numbers for each "slot" after each step.

5 choices for the first slot
5 choices for the second slot,
5 choices for the third slot,
5 choices for the fourth slot,
and 5 choices for the fifth slot

5*5*5*5*5 = 5^5 = 3125

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