GATE EC 2019 Set 1 — Question 4
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General Aptitude → Quantitative Aptitude → Permutations & Combinations
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Question
Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second, respectively from the right side of the shelf. The number of different orders in which P, Q and T may be arranged is __________.
Correct answer
(B) 6
Solution
The total number of books is 5: P, Q, R, S, T.
The problem states that books R and S are to be arranged first and second, respectively, from the right side of the shelf.
Let's visualize the shelf with 5 positions:
_
From the right side, the first position is R and the second is S:
_ S R
Now, the remaining books are P, Q, and T. There are 3 remaining positions for these 3 books.
The number of different ways to arrange 3 distinct items in 3 distinct positions is given by (3 factorial).
.
Therefore, P, Q, and T can be arranged in 6 different orders.The final answer is
The problem states that books R and S are to be arranged first and second, respectively, from the right side of the shelf.
Let's visualize the shelf with 5 positions:
_
From the right side, the first position is R and the second is S:
_ S R
Now, the remaining books are P, Q, and T. There are 3 remaining positions for these 3 books.
The number of different ways to arrange 3 distinct items in 3 distinct positions is given by (3 factorial).
.
Therefore, P, Q, and T can be arranged in 6 different orders.The final answer is
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