Question

in how many ways can the letter of the words 'CABLE' be arranged so that the vowels always occupy odd spaces​

Answer 1

Answer:

36

Step-by-step explanation:

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Answer 2

Given:

A word cable is arranged such that the vowels occupy the odd spaces.

To Find:

The total number of ways such that the vowels occupy the odd spaces.

Solution:

The given question can be solved by using the concepts of permutations and combinations.

1. The given word is CABLE. It contains 5 letters.

2. The odd positions are 1,3 and 5. The even positions are 2 and 4.

3. The vowels from the given word CABLE are A and E, and the consonants are C, B, and E.

4. According to the properties of Permutations and Combinations,

• Let there are n objects which are to be filled in our places such that each place, occupies only one object, then the number of ways of arranging objects are nCr.

• nCr = [(n!)/(n-r)! * r!]   (! Is the notation of factorial, n! = n * (n-1) * (n-2) *…* 1).

5. The two vowels can be occupied in three odd spaces in 3C2 ways. The three consonants can be arranged in 3! Factorial ways in the remaining 3 spaces.

6. The two mobiles can also interchange among themselves, therefore the total number of possibilities is 2 * 3C2 * 3!  

=> 2 * 3C2 * 3!,

=> 2 * (6/2) * 6,

=> 6 * 6,

=> 36 ways.

Therefore, the total number of arrangements is 36.