Example 1 :
In how many several way the word KOLKATA can be prepared so that as vowel always come together?
Answer:
First of all we need to know how many vowel in this given word, here is three vowel that is O and A,A.
then we count the consonant that is four.Now we count the number of vowel as a single unit that is vowel O A,A count as single unit and add it with consonant so we have a four unit.
(4 consonant +three vowel as single unit ) = 5 x 3( three vowel)
5! x 3! = 1 x 2 x 3 x 4 x 5 x 1 x 2 x 3 = 720 ways we prepared the word.
Example 2 :
In how many ways can 6 apples be distributed among 5 boys , there being no restriction to the number of apples each boy may get ?
Answer :
Any of the 5 boys get each apple and this can be done in 5 ways
The number of ways is = 56 = 15625 .
Example 3 :
In how many several way the word HOUSE can be prepared so that as vowel always come together?
Answer :
First of all we need to know how many vowel in this given word, here is three vowel that is E ,O and U.
then we count the consonant that is Two.Now we count the number of vowel as a single unit that is vowel E,O and U count as single unit and add it with consonant so we have a three unit.
(2 consonant + three vowel as single unit ) = 3 x 3( three vowel)
3! x 3! = 1 x 2 x 3 x 1 x 2 x 3 = 36 ways we prepared the word.
Example 4: In how many several ways the word CAME can be arranged,that the vowels not come together?
Answer : First of all we need to know how many vowel in this given word, here is two vowel that is A and E.
then we count the consonant that is Two.Now we count the number of vowel as a single unit that is vowel A and E count as single unit and add it with consonant so we have a three unit.
(2 consonant + two vowel as single unit ) = 3 x 2( two vowel)
Note: If we Subtract total number ways from within vowel ways than we get the not come to-gather ways,
So, ( 4! – 3! x 2! ) = 12.
Example 5: In how many several ways the word HATE can be arranged, that the vowels not come together?
Answer : First of all we need to know how many vowel in this given word, here is two vowel that is A and E.
then we count the consonant that is Two.Now we count the number of vowel as a single unit that is vowel A and E count as single unit and add it with consonant so we have a three unit.
(2 consonant + two vowel as single unit ) = 3 x 2( two vowel)
Note: If we Subtract total number ways from within vowel ways than we get the not come together ways,
So, ( 4! – 3! x 2! ) = 12
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