Question

An academic department has just completed voting by secret ballot for a departmenthead. The ballot box contains four slips with votes for candidate A and three slips with votes for candidate B. Suppose these slips are removed from the box one by one, What isthe total number of possible outcomes?

Answer 1

Answer: 35

Step-by-step explanation:

Given : An academic department has just completed voting by secret ballot for a department head.

The ballot box contains 4 slips with votes for candidate A and 3 slips with votes for candidate B.

Total slips = 7

The permutations of 'n' things from which 'a' things are like , 'b' things are like is given by :-

$\dfrac{n!}{a!\ b!}$

Now, the total number of possible outcomes for the given situation will be:

$\dfrac{7!}{4!\ 3!}=\dfrac{7\times6\times5\times4!}{3\times2\times1\times\ 4!}\\\\=35$

Hence, the total number of possible outcomes =35