Question

Find the number of “words” with four distinct letters that can be made from the letters "ORANGES"?

Answer 1

See explanation.

Explanation:

To find the total number of "words" we can think of in how many ways each letter can be chosen.

• the first letter can be chosen from among `7` letters,

• the second letter can be chosen from all letters except the one chosen before, so there are `6` possibilities,

• the third letter can be chosen in `5` ways (2 letters have already been used)

• the fourth (and last) letter can be chosen from `4` letters left.

Now to find the total number of possible choices we have to multiply all the numbers from the previous points:

`n=7*6*5*4=840`

Answer: There are `840` possible "words".

Answer 2

840 ways

Explanation:

An alternate way to arrive at this solution is to see that it is a permutation question (we care about the order in which the letters are placed), the general formula of which is:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

Here we have `n=7 and k=4`

`P_(7,4)=(7!)/(3!)=5040/6=840`