SIVA and Shyam are playing chess together. SIVA known the two rows in which he has to put all the pieces in but he doesn’t know how to place them. What is the probability that he puts all the pieces in the right place?Options8!/16!8!/15!(2𝑥8!)/16!8!/(2𝑥15!)
Question
SIVA and Shyam are playing chess together. SIVA known the two rows in which he has to put all the pieces in but he doesn’t know how to place them. What is the probability that he puts all the pieces in the right place?Options8!/16!8!/15!(2𝑥8!)/16!8!/(2𝑥15!)
Solution
The game of chess involves 16 pieces for each player: 1 king, 1 queen, 2 rooks, 2 knights, 2 bishops, and 8 pawns.
Assuming SIVA knows the two rows in which he has to put all the pieces, but doesn't know how to place them, he has to arrange 16 pieces in 16 places.
The total number of ways to arrange 16 unique items is 16!, which is 16 factorial, or 161514*...21.
However, there are some pieces that are identical. There are 8 pawns which are identical, and 2 rooks, 2 knights, and 2 bishops which are identical.
So, the number of ways to arrange these identical pieces is 8! for the pawns, and 2! for each of the rooks, knights, and bishops.
Therefore, the total number of distinct arrangements of the chess pieces is 16! / (8! * 2! * 2! * 2!).
The probability that SIVA puts all the pieces in the right place is therefore 1 / (16! / (8! * 2! * 2! * 2!)), which simplifies to (8! * 2! * 2! * 2!) / 16!.
So, the correct answer is not in the options given.
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