Find the number of “words” with four distinct letters that can be made from the letters "ORANGES"?
2 Answers
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:
Answer: There are
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:
Here we have