The value of 13C2 + 13C3 + 13C4 + … + 13C13 is

• A 2¹³ − 13 B 2¹³ − 14
• Can odd number ≠ 2¹³ − 12
• Can even number ≠ 2¹³ − 14

To solve the expression 13C2 + 13C3 + 13C4 + … + 13C13, we can use the properties of binomial coefficients. The sum of all the binomial coefficients from 0 to n is equal to 2^n. In this case, for n = 13, we have:

Calculating the Total

The total sum of all coefficients from 0 to 13 is:

2¹³ = 8192

Excluding the First Two Terms

We need to exclude the terms 13C0 and 13C1 from the total:

• 13C0 = 1
• 13C1 = 13

So, the sum we want is:

13C2 + 13C3 + ... + 13C13 = 2¹³ - 1 - 13 = 2¹³ - 14

Final Answer

The value of 13C2 + 13C3 + 13C4 + … + 13C13 is:

2¹³ - 14