A lot of national flags are made up of three horizontal stripes.

How many different three colour flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colours must be different?

How many of them contain a red stripe?

How many extra possibilities are there if the top colour can be the same as the bottom colour?

3 marks

On his university application, Prashad must list his course choices in order of preference.

He must choose four of the six courses available in his major discipline and three of the four courses offered in related subjects.

In how many ways can Prashad list his course choices? Explain the reasoning for your answer.

Question

Mathematics

Goodwin

25 March, 23:37

A lot of national flags are made up of three horizontal stripes.

How many different three colour flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colours must be different?

How many of them contain a red stripe?

How many extra possibilities are there if the top colour can be the same as the bottom colour?

3 marks

On his university application, Prashad must list his course choices in order of preference.

He must choose four of the six courses available in his major discipline and three of the four courses offered in related subjects.

In how many ways can Prashad list his course choices? Explain the reasoning for your answer.

+5

Answers (1)

Know the Answer?

Jordyn Velez · Answer 1

How many different three colour flags (tricolors) can be designed using green, blue, red, yellow and black stripes if all three colours must be different?

6P3 = 6! / (6 - 3) ! = 6!/3! = (6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 720/6 = 120 flags.

How many of them contain a red stripe?

The remaining two colours can be arranged in 5P2 = 5! / (5 - 2) ! = 5!/3! = (5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 120/6 = 20ways

The red stripe can arranged in 3 ways

Therefore, number of flags having red stripe is 20 x 3 = 60 flags.