Question

in how many can the letters of the word'FAILURE' be arranged so that the consonants may occupy only odd positions

Answer 1

Hey..!

Here’s ur answer..

Answer is 576.

There are seven letters in the word ‘FAILURE’ out of which the consonants are- F, L and R. And the vowels are A,E,I and U. There are total 4 odd positions (1st, 3rd, 5th and 7th) and 3 even positions (2nd, 4th and 6th) to fill.

The constraint is that consonants may occupy only an odd position. So, first we’ll fill the odd positions with the consonants. There are total 4 odd positions and 3 consonants. Since there are only 3 consonants, then at a time, 3 consonants can occupy only 3 odd positions and one will be left out. So, we’ll need to select which three odd positions out of the four available odd positions we will fill first. The number of ways of selecting 3 odd positions out of four are:

(43)=(43)=4!3!(4–3)!
(
4
3
)
=
(
4
3
)
=
4
!
3
!
(
4
–
3
)
!

This gives us 4 ways to select 3 odd positions out of the available 4 odd positions. Now that we have selected the odd positions to fill, we now need to arrange the consonants in these positions. The number of ways in which we can arrange 3 consonants is equal to 3!.

Now only the vowels remain to be arranged. There are 4 vowels and 4 vowels can be arranged in 4!
Now we multiply these results to arrive at the answer: 4∗3!∗4!=576
4
∗
3
!
∗
4
!
=
576
ways.

Hope this helps u..
#bipasha

Answer 2

Answer:

The answer of the question is:-

We can arrange the word FALIURE in 576 ways.

Step-by-step explanation:

From the given data in the question, we have got that:-

In this word FALIURE the number of vowels are 4 and the number of consonants are 3.

There are 4 odd positions in this word FALIURE and we have to arrange 3 consonants in this 4 places.

So we can arrange those 3 word in :

= 4*3*2 ways

4*3*2 ways =24 ways.

Also for the remaining 3 positions in this word there are 4 vowels in this word,

So we can arrange those vowels in= 4*3*2 ways

= 24 ways.

So,the total number of ways to arrange the word FALIURE is = 24*24= 576 ways

This is the required solution for this question.

So,We can arrange the word FALIURE in 576 ways.

To know more about Permutations and Combinations problem,visit the given link below:-

https://brainly.in/question/3116555

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