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How many batting orders are possible for the Indian cricket team if there is a squad of 15 to choose from such that Sachin Tendulkar is always chosen?
- a)1001 x 11!
- b)364 x 11!
- c)11!
- d)15 x 11!
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
How many batting orders are possible for the Indian cricket team if t...
15-1C11-1 x 11!
⇒ 14C10 x 11! = 1001 x 11!
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Solution:
Given that Sachin Tendulkar is always chosen, we have 14 players left to choose from.
We need to find the number of possible batting orders, which is the number of ways we can arrange these 14 players in a line-up.
This can be done using the formula for permutations of n objects taken r at a time, which is:
nPr = n! / (n - r)!
In this case, we need to find the number of permutations of 14 players taken 10 at a time (since a batting order has 11 players, including Sachin).
So, the number of batting orders possible is:
14P10 = 14! / 4!
= 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5
= 1001 x 11!
Therefore, the correct option is (a) 1001 x 11!.
Given that Sachin Tendulkar is always chosen, we have 14 players left to choose from.
We need to find the number of possible batting orders, which is the number of ways we can arrange these 14 players in a line-up.
This can be done using the formula for permutations of n objects taken r at a time, which is:
nPr = n! / (n - r)!
In this case, we need to find the number of permutations of 14 players taken 10 at a time (since a batting order has 11 players, including Sachin).
So, the number of batting orders possible is:
14P10 = 14! / 4!
= 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5
= 1001 x 11!
Therefore, the correct option is (a) 1001 x 11!.
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How many batting orders are possible for the Indian cricket team if there is a squad of 15 to choose from such that Sachin Tendulkar is always chosen?a)1001 x 11!b)364 x 11!c)11!d)15 x 11!Correct answer is option 'A'. Can you explain this answer?
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