Question

How many words can be formed the letter of the word trapezium selecting 2 vowels and 3consonants so that no letter is repeated in any word ?

Answer 1

Answer:

7200

Step-by-step explanation:

So we're specifically looking for 5 letter words that have 2 vowels and 3 consonants.

One way to go about this is to select the letter first and then place them on the page.

There are 4 vowels (a, e, i, u) and we want to choose 2 (different) ones from them.  The number of ways of doing this is "4 choose 2" = 6.  (Get this from Pascal's Triangle.)

There are 5 consonants (t, r, p, z, m) and we want to choose 3 (different) ones from them.  The number of ways of doing this is "5 choose 3" = 10.

Now that we've got our 5 letters, let's put them into our 5 positions, one at a time.

There 5 ways of choosing the first letter (from the 5 letters that we've selected), then 4 ways of choosing the second letter, then 3, then 2 and then 1 for the final position.  So there are 5! = 120 ways of putting the letters in place once we've selected what letters to use.

In total, the number of words is then

6 x 10 x 120 = 7200