A political polling organization wishes to select a smaller focus group from a group of 7 Republicans, 10 Democrats, and 2 Independents. In how many ways can the group be chosen if: (a) it will consist of 1 Republican and 4 Democrats?(b) it will consist of 2 Republicans, 2 Democrats, and 3 Independents?

a) 1470 ways

b) 2835 ways

Step-by-step explanation:

the question is not correct, in the correct question The number of independents should be 3 not 2

there are 7 republicans, 10 democrats and 3 independents.

C(n,r) is the number of different combinations of n distinct objects taken r at a time.

C(n,r) =

a) it will consist of 1 Republican and 4 Democrats

The number of ways this can be chosen is = C(7,1) × C(10,4) = = 7 × 210 = 1470 ways

(b) it will consist of 2 Republicans, 2 Democrats, and 2 Independents (consist of 2 independents not 3)

The number of ways this can be chosen is = C(7,2) × C(10,2) × C(2,2)

 = = 21 × 45 × 3 = 2835 ways

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.