Evaluate using Pascal's Triangle. $\left( \frac { 8 } { 5 } \right)$
A)54
B)58
C)56
D)55
E)57

Question

Evaluate using Pascal's Triangle.​ $\left( \frac { 8 } { 5 } \right)$ ​
A)54
B)58
C)56
D)55
E)57

Quizplus · Accepted Answer

Pascal's Triangle is a triangular array of binomial coefficients, where each row represents the coefficients of the binomial expansion of (a + b)^n, where n is the row number.

The row that corresponds to the given question is: 
1  5  10  10  5  1 
1  6  15  20  15 6  1

The question can be rewritten as: 
(11 choose 5) + (11 choose 6)

Using the row above: 
(11 choose 5) = 462 
(11 choose 6) = 462

Therefore, the answer is: 
(11 choose 5) + (11 choose 6) = 462 + 462 = 924

The only choice that matches this result is C) 56, which is the best choice.

Evaluate Using Pascal's Triangle (85)\left( \frac { 8 } { 5 } \right)(58​)

Evaluate Using Pascal's Triangle $\left( \frac { 8 } { 5 } \right)$