Select the correct answerSIVA 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!/15!8!/(2𝑥15!)8!/16!(2𝑥8!)/16!
Question
Select the correct answerSIVA 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!/15!8!/(2𝑥15!)8!/16!(2𝑥8!)/16!
Solution
The correct answer is 8!/16!.
Here's why:
In a game of chess, each player starts with 16 pieces: 1 king, 1 queen, 2 rooks, 2 knights, 2 bishops, and 8 pawns.
If SIVA knows the two rows where he has to place all the pieces but doesn't know how to arrange them, then he is essentially trying to arrange 16 unique items (the chess pieces) in 16 spots (the squares on the two rows).
The total number of ways to arrange 16 unique items in 16 spots is 16!, which is the denominator in our probability fraction.
The number of ways to correctly arrange the pieces is just 1 (since there's only one correct arrangement), but since each piece is not unique (for example, there are 8 identical pawns), we have to divide by the number of ways to arrange these identical pieces.
The number of ways to arrange 8 pawns is 8!, and the number of ways to arrange the 2 rooks, 2 knights, and 2 bishops (which are also identical) is 2! for each pair. So, the total number of ways to arrange the identical pieces is 8! * 2! * 2! * 2! = 8!.
So, the probability that SIVA puts all the pieces in the right place is the number of correct arrangements divided by the total number of arrangements, which is 8!/16!.
Similar Questions
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?
Select the correct answerRAMU can hit a target 3 times in 6 shots, SIVA can hit the target 2 times in 6 shots and SHYAM can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the targetOptions1/32/35/25/6
Select the correct answerIn a row of children, Ravi is 24 from right and Sham is 17 from left. When they interchange positions Ravi is 38 from right. What will be Shyam‘s present position from the left end?Options3133None3234
RAMU can hit a target 3 times in 6 shots, SIVA can hit the target 2 times in 6 shots and SHYAM can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target
You and your friend are two of eight servers working a shift in a restaurant. At the beginning of the shift, the manager randomly assigns one section to each server. Find the probability that you are assigned Section 1 and your friend is assigned Section 2. Express you answer as a fraction in simplest form.The probability is .
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.