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The sum of the binomial coefficients of the 3rd, 4th terms from the beginning and from the end of (a + x)n is 440 then n =
- a)10
- b)11
- c)12
- d)13
Correct answer is option 'B'. Can you explain this answer?
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The sum of the binomial coefficients of the 3rd, 4th terms from the be...
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Explanation:
Given:
Sum of binomial coefficients of 3rd and 4th terms from the beginning and from the end of (a + x)^n is 440.
Formula:
The binomial coefficient formula is given by:
C(n, k) = n! / (k! * (n-k)!)
Approach:
1. We need to find the binomial coefficients of the 3rd and 4th terms from both ends.
2. Calculate the sum of these coefficients and equate it to 440.
3. Solve for 'n'.
Calculation:
1. The binomial coefficients of the 3rd and 4th terms from the beginning are C(n, 2) and C(n, 3) respectively.
2. The binomial coefficients of the 3rd and 4th terms from the end are C(n, n-2) and C(n, n-3) respectively.
3. Sum of these coefficients: C(n, 2) + C(n, 3) + C(n, n-2) + C(n, n-3) = 440
4. Simplify the expression and solve for 'n'.
Answer:
After solving the equation, we find that n = 11. Therefore, the correct answer is option 'B'.
Given:
Sum of binomial coefficients of 3rd and 4th terms from the beginning and from the end of (a + x)^n is 440.
Formula:
The binomial coefficient formula is given by:
C(n, k) = n! / (k! * (n-k)!)
Approach:
1. We need to find the binomial coefficients of the 3rd and 4th terms from both ends.
2. Calculate the sum of these coefficients and equate it to 440.
3. Solve for 'n'.
Calculation:
1. The binomial coefficients of the 3rd and 4th terms from the beginning are C(n, 2) and C(n, 3) respectively.
2. The binomial coefficients of the 3rd and 4th terms from the end are C(n, n-2) and C(n, n-3) respectively.
3. Sum of these coefficients: C(n, 2) + C(n, 3) + C(n, n-2) + C(n, n-3) = 440
4. Simplify the expression and solve for 'n'.
Answer:
After solving the equation, we find that n = 11. Therefore, the correct answer is option 'B'.
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