# how many words of 3 distinct letter can be formed from alphabet (a, b, g, z) = a.) 24 b.) 36 c.) 5 d.) 4

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### 3 Answers

To determine the number of words using an alphabet of distinct letters, we are looking to find a permutation. The number of permutations of n elements to find a subset of size r is given by:

`P(n,r)={n!}/{(n-r)!}`

where the ! indicates the factorial function. That is:

`n! =n times (n-1) times (n-2) times cdots times 3 times 2 times 1`

In this case, we have an alphabet of 4 elements and are looking for the number of words of 3 letters. This means n=4 and r=3 to get:

`P(4,3)={4!}/{1!}`

`=4 times 3 times 2`

`=24`

**There are 24 possible words, which is option a.**

The number of ways of arranging r different elements from a set of n distinguishable elements is given by `P(n, r) = (n!)/((n-)r!)`

To form words with 3 distinct letters from the set of letters made up of {a, b, g, z}, 3 letters have to be arranged from the 4 letters given. This can be done in `P(4, 3) = (4!)/((4-3)!) = 4*3*2 = 24` ways.

**The correct answer is option a.**

a.) 24