Question

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

• A. 576
• B. ${}^4{C}_3.(4!)$
• C. $2(4!)$
• D. none of these

Answer 1

The correct option is A 576

The even places can be occupied only by consonants (RTCL)
we select 3 out of 4 to occupy these 3 places ${=}^4{C}_3=4$
They can themselves arrange in $3!$ ways $=6$ ways
total $=6.4$ ways $=24$ ways

For the odd places remaining 4 letters will arrange themselves in $4!$ ways $=24$ ways

So, total $=24.24$ ways $=576$ ways