The program manager for an amateur performance night auditioned 12 acts, but there is only room for 3 acts on the program. How many different ways can the program manager arrange 3 different acts from the original 12

There are 220 different ways to arrange the acts.

Step-by-step explanation:

The order in which the acts are arranged is not important, so we use the combinations formula to solve this question.

Combinations Formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

How many different ways can the program manager arrange 3 different acts from the original 12

Three acts from a set of 12. So

There are 220 different ways to arrange the acts.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

step-by-step explanation: