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.
$$^4{C_3} \times \left( {4!} \right)$$
C.
$$2(4!)$$
D.
None of these
Answer :
$$576$$
Solution :
The number of ways to fill the three even places by 4 consonants $$ = {\,^4}{P_3}.$$
After filling the even places, remaining places can be filled in $${\,^4}{P_4}$$ ways.
So, the required number of words $$ = {\,^4}{P_3} \times {\,^4}{P_4}.$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
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