Question

How many words can be made from the letters of the word DAUGHTER assuming that no

letter is repeated ? How many words can be made from this word in which so that

consonants and vowels occupy their own place ?​

Answer 1

Step-by-step explanation:

red, get, rat, hat, hate and some more

Answer 2

The letters of the word daughter are “d,a,u,g,h,t,e,r”.

So, the vowels are ‘a, u, e’ and the consonants are “d,g,h,t,r”.

(i)Now, all the vowels should come together, so consider the bundle of vowels as one letter, then total letters will be 6.

So, the number of words formed by these letters will be 6!

but, the vowels can be arranged differently in the bundle, resulting in different words, so we have to consider the arrangements of the 3 vowels.

So, the arrangements of vowels will be 3!

Thus, the total number of words formed will be equal to (6!×3!)=4320

(ii)First arrange 5 consonants in five places in 5! ways.

6 gaps are created. Out of these 6 gaps, select 3 gaps in

6

C

3

ways and then make the vowels permute in those 3 selected places in 3! ways.

This leads 5!×

6

C

3

×3!=14400.

HOPE IT HELPED...