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The number of combinations that can be made by taking 4 letters of the word 'COMBINATION'
- a)70
- b)63
- c)3
- d)136
Correct answer is option 'D'. Can you explain this answer?
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The number of combinations that can be made by taking 4 letters of the...
Solution:
To find the number of combinations that can be made by taking 4 letters of the word COMBINATION, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items chosen, and ! denotes factorial (the product of all positive integers up to that number).
Step 1: Count the total number of letters in the word COMBINATION
The word COMBINATION has a total of 10 letters.
Step 2: Determine the number of ways to choose 4 letters from the 10 letters
Using the formula for combinations, we can compute as follows:
10C4 = 10! / 4!(10-4)! = 10! / 4!6! = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210
Therefore, there are 210 possible combinations of 4 letters that can be made from the word COMBINATION.
Step 3: Choose the correct option from the given choices
The correct option is D, which states that the number of combinations is 136. This is incorrect as we have found that there are 210 possible combinations, not 136.
Hence, the correct answer is option 'A', which states that the number of combinations is 70.
To find the number of combinations that can be made by taking 4 letters of the word COMBINATION, we can use the formula for combinations:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items chosen, and ! denotes factorial (the product of all positive integers up to that number).
Step 1: Count the total number of letters in the word COMBINATION
The word COMBINATION has a total of 10 letters.
Step 2: Determine the number of ways to choose 4 letters from the 10 letters
Using the formula for combinations, we can compute as follows:
10C4 = 10! / 4!(10-4)! = 10! / 4!6! = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210
Therefore, there are 210 possible combinations of 4 letters that can be made from the word COMBINATION.
Step 3: Choose the correct option from the given choices
The correct option is D, which states that the number of combinations is 136. This is incorrect as we have found that there are 210 possible combinations, not 136.
Hence, the correct answer is option 'A', which states that the number of combinations is 70.
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The number of combinations that can be made by taking 4 letters of the...
Option D 136 is the correct answer
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The number of combinations that can be made by taking 4 letters of the wordCOMBINATIONa)70b)63c)3d)136Correct answer is option 'D'. Can you explain this answer?
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