Mark the correct alternative in the following: The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is

Question

Philoid · Accepted Answer

We have, 7 objects {A}, {R}, {T}, {I}, {C}, {L}, {E} and there are 4 consonants {R}, {T}, {C}, {L}; and the 3 out of 4 of the consonants should occupy even places i.e. 2, 4 and 6^th place, this can be done in

= 24 ways.

And, the other 4 alphabets i.e. the remaining 1 consonant and 3 vowels is to be placed in 4 places in ⁴P₄ = 4! = 24 ways.

So, the number The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is

= 576.

Mark the correct alternative in the following:The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is

Mark the correct alternative in the following:
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is