Question

Using the binomial theorem, in how many ways can a campaign manager assign 15 campaigners to three matatus when 6 are in the first matatu, 5 in the second matatu, and 4 in the third matatu?

Answer 1

Using the binomial theorem, there are 5005 different ways for the campaign manager to assign the 15 campaigners to the three matatus.

Step-by-step explanation:

In this problem, we can use the binomial theorem to determine the number of ways to assign the campaigners to the matatus.

The binomial theorem states that for a given number of objects to be distributed among a fixed number of containers, the total number of possible arrangements is given by the formula (n choose k) = (n!)/(k!(n-k)!), where n represents the total number of objects, and k represents the number of objects in each container.

In this case, there are 15 campaigners in total, and they need to be assigned to three matatus with 6, 5, and 4 campaigners respectively.

So, the number of ways to assign the campaigners would be (15 choose 6)*(9 choose 5)*(4 choose 4).

Using the binomial theorem, we can calculate the number of ways as:

(15 choose 6)*(9 choose 5)*(4 choose 4) = (15!)/(6!(15-6)!)*(9!)/(5!(9-5)!)*(4!)/(4!(4-4)!)

= (15!)/(6!*9!)*(9!)/(5!*4!)*(4!)/(4!)

= (15*14*13*12*11*10)/(6*5*4*3*2*1)*(9*8*7*6*5)/(5*4*3*2*1)*(4*3*2*1)/(4*3*2*1)

= 5005

Therefore, there are 5005 different ways for the campaign manager to assign the 15 campaigners to the three matatus.