14 students have volunteered for a committee. Eight of them are seniors and six of them are juniors. (a) How many ways are there to select a committee of 5 students

Explanation:

We have five slots to fill, which I'll label A through E.

There are,

Each time we fill up a slot, we count down by 1.

This gives 14*13*12*11*10 = 240,240 different permutations. If order mattered, then this would be the answer.

However, order doesn't matter on a committee without rankings. Each member has the same rank as any other.

Within any group of 5 people, there are 5! = 5*4*3*2*1 = 120 ways to arrange them. This means we divide that 240,240 figure by 120 to find the number of combinations.

There are (240,240)/(120) = 2002 different combinations.

Here's how we could have done the problem using the nCr combination formula.

Plug in n = 14 and r = 5.

n C r = (n!)/(r!(n-r)!)

14 C 5 = (14!)/(5!*(14-5)!)

14 C 5 = (14!)/(5!*9!)

14 C 5 = (14*13*12*11*10*9!)/(5!*9!)

14 C 5 = (14*13*12*11*10)/(5!)

14 C 5 = (14*13*12*11*10)/(5*4*3*2*1)

14 C 5 = (240240)/(120)

14 C 5 = 2002

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

h/o/e/s mad

step-by-step explanation:

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