Since there are two competitions, one for boys and one for girls, and we want all the possible results we will calculate the possible combinations for the boys and multiply them by the possible combinations for the girls. This is shown below:

$Boys = \frac{15!}{3!(15 - 3)!} = \frac{15!}{3!12!} = \frac{15*14*13*12!}{3!12!}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = \frac{15*14*13}{3*2*1}\\Boys = 455$

$Girls = \frac{4!}{3!*(4 - 3)!}\\Girls = \frac{4*3!}{3!}\\Girls = 4$

Total number of possible results:

$results = 4*455\\results = 1820$

3 0

4 years ago

Seven more than the product of a number and 5 equals 2 . Use the variable c for the unknown number.

svetoff [14.1K]

Answer:

Equation: 5c + 7 = 2

Solution: The number is -1.

Step-by-step explanation:

The unknown number is c.

"the product of a number and 5" is 5c

"Seven more than the product of a number and 5" is 5c + 7

"Seven more than the product of a number and 5 equals 2" is 5c + 7 = 2

The equation is

5c + 7 = 2

To solve, we first subtract 5 from both sides.

5c + 7 - 7 = 2 - 7

5c = -5

Now divide both sides by 5.

5c/5 = -5/5

c = -1

Answer: The number is -1.

7 0

4 years ago