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The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, is
- a)165
- b)364
- c)1001
- d)1365
Correct answer is option 'C'. Can you explain this answer?
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The number of ways in which a cricket team of 11 players be chosen out...
If captain is always included then we can choose 10 more players out of the remaining 14 players. So
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The number of ways in which a cricket team of 11 players be chosen out...
Number of ways to choose a cricket team with a captain included
To solve this problem, we can apply the concept of combinations. We need to choose 11 players out of a batch of 15, with the condition that the captain is always included.
Step 1: Choose the captain
Since the captain is always included, we have only one option for this position.
Step 2: Choose the remaining 10 players
Now, we need to choose 10 players from the remaining 14 players (excluding the captain). This can be done in combination.
The number of ways to choose r objects from a set of n objects is given by the combination formula: nCr = n! / (r!(n-r)!), where n! denotes the factorial of n.
In this case, we need to choose 10 players from a group of 14 players. Therefore, the number of ways to choose the 10 players is:
14C10 = 14! / (10!(14-10)!) = 14! / (10!4!) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) = 1001
Step 3: Multiply the choices from step 1 and step 2
Since both steps are independent events, we can multiply the number of choices from step 1 and step 2 to get the total number of ways to choose the team.
Total number of ways = 1 * 1001 = 1001
Therefore, the correct answer is option C) 1001.
To solve this problem, we can apply the concept of combinations. We need to choose 11 players out of a batch of 15, with the condition that the captain is always included.
Step 1: Choose the captain
Since the captain is always included, we have only one option for this position.
Step 2: Choose the remaining 10 players
Now, we need to choose 10 players from the remaining 14 players (excluding the captain). This can be done in combination.
The number of ways to choose r objects from a set of n objects is given by the combination formula: nCr = n! / (r!(n-r)!), where n! denotes the factorial of n.
In this case, we need to choose 10 players from a group of 14 players. Therefore, the number of ways to choose the 10 players is:
14C10 = 14! / (10!(14-10)!) = 14! / (10!4!) = (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1) = 1001
Step 3: Multiply the choices from step 1 and step 2
Since both steps are independent events, we can multiply the number of choices from step 1 and step 2 to get the total number of ways to choose the team.
Total number of ways = 1 * 1001 = 1001
Therefore, the correct answer is option C) 1001.
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The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, isa)165b)364c)1001d)1365Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, isa)165b)364c)1001d)1365Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of ways in which a cricket team of 11 players be chosen out of a batch of 15 players so that the captain of the team is always included, isa)165b)364c)1001d)1365Correct answer is option 'C'. Can you explain this answer?.
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