Example 1
seven speed skaters are competing in an olympic race. the first-place skater earns the gold medal, the second-place skater earns the silver medal, and the third-place skater earns the
bronze medal. in how many different ways could the gold, silver, and bronze medals be awarded? the letters a, b, c, d, e, f, and g will be used to represent these seven skaters.
how can we determine the number of different possible outcomes? how many are there?
now consider a slightly different situation. seven speed skaters are competing in an olympic race. the top three skaters move on to the next round of races. how many different
"top three" groups can be selected?
how is this situation different from the first situation? would you expect more or fewer possibilities in this situation? why?
would you consider the outcome where skaters b, c, and a advance to the final to be a different outcome from a, b, and c advancing?
a permutation is an ordered arrangement (a sequence) of items from a set of nn distinct items.
in contrast, a combination is an unordered collection (a set) of items from a set of nn distinct items.
when we wanted to know how many ways there are for seven skaters to finish first, second, and third, order was important. this is an example of a permutation of 3 selected from
a set of 7. if we want to know how many possibilities there are for which three skaters will advance to the finals, order is not important. this is an example of a combination of 3 selected
from a set of 7.

answer: plz give a pic and answer choices so i can answer!

step-by-step explanation:

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.