Next year you are taking math, English, history, keyboarding, chemistry,physics and physical education. Each class is offered during each of the seven periods in the day. In how many different orders can you schedule your classes.
How many different signals can be made by displaying five flags all at one time on a flagpole? The flags differ only in color: two are red, two are white, and one is blue.
How many 7-digit telephone numbers can be created if the first digit must be 8, the second must be 5, and the third must be 2 or 3.
Explain how you got the answer, I would appreciate it.
How many different signals can be made by displaying five flags all at one time on a flagpole? The flags differ only in color: two are red, two are white, and one is blue.
How many 7-digit telephone numbers can be created if the first digit must be 8, the second must be 5, and the third must be 2 or 3.
Explain how you got the answer, I would appreciate it.
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#1.
7! = 5040
Explanation: 7 possible periods for the first class you choose a time for, then once that time is chosen, there are 6 remaining possible times for the next class, and so on.
#2. So the flags hang at different heights on the pole? Then we're counting the ways to order them. But it's less than 5! because some of the flags are indistinguishable with another flag.
There are 5 possible spots for the blue flag.
Then once that spot is chosen, there are 4C2 = 6 possible spots for the red flags.
Then once those spots are chosen, there are 2 spots remaining and the white flags must go there.
5 * 4C2 = 30
#3.
There are 2 possibilities for the 3rd digit.
Then for the next four there are 10^4 possibilities (10 possibilities for each digit).
2 * 10^4 = 20,000
7! = 5040
Explanation: 7 possible periods for the first class you choose a time for, then once that time is chosen, there are 6 remaining possible times for the next class, and so on.
#2. So the flags hang at different heights on the pole? Then we're counting the ways to order them. But it's less than 5! because some of the flags are indistinguishable with another flag.
There are 5 possible spots for the blue flag.
Then once that spot is chosen, there are 4C2 = 6 possible spots for the red flags.
Then once those spots are chosen, there are 2 spots remaining and the white flags must go there.
5 * 4C2 = 30
#3.
There are 2 possibilities for the 3rd digit.
Then for the next four there are 10^4 possibilities (10 possibilities for each digit).
2 * 10^4 = 20,000