A town orchestra needs 3 new flute players and 4 new trumpet players. 8 flutists and 11 trumpeters try out, then the orchestra should select 3 flutists from 8 and 4 trumpeters form 11.

They can choose 3 flutists from 8 in

$C_8^3=\dfrac{8!}{3!(8-3)!}=\dfrac{8!}{3!\cdot 5!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8}{1\cdot 2\cdot 3\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5} =56$ ways.

They can choose 4 flutists from 11 in

$C_{11}^4=\dfrac{11!}{4!(11-4)!}=\dfrac{11!}{4!\cdot 7!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11}{1\cdot 2\cdot 3\cdot 4\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7} =330$ ways.

Use the product rule: 56·330=18480 ways for conductor to choose his new members.

3 0

3 years ago

On a sunny day, a tree casts a shadow that is 146 feet long. At the same time, a person who is 5.6

iVinArrow [24]

Let X = tree height.

X/146 = 5.6/11.2

3 0

3 years ago

One year, the population of a city was 201,000. Several years later it was 237,180. Find the percent increase.

exis [7]

Answer:

18%

Step-by-step explanation:

% increase = new population - old population x 100

old population. 1

% increase = 237180 - 201000 x 100

201000. 1

% increase = 36180 x 100

201000

% increase = 3618000

201000

% increase = 18%

5 0

2 years ago

H(x)=(x+5) ^2

Advocard [28]

The answer is 10
............

5 0

3 years ago