Since only one person can finish in first place, one in second, etc., the total number of placers is 12x11x10, or
1320 different ways
the 12 racers can finish 1st, 2nd and 3rd….
How many ways can 1st 2nd AND 3rd be given in a race out of 12?
Given the identity of the horse that comes second, the horse that comes third can be any of the remaining 10 horses. So the number of different ways in which 1st, 2nd and 3rd can occur is
12 x 11 x 10 = 1,320
.
How many ways can 8 horses finish a race?
There are
336 ways
to have 8 horses place for 1st, 2nd, and 3rd place. The work above demonstrates how one can simplify the problem using the permutation formula.
How many ways can 9 horses finish a race?
=
5040
. Nine horses are running in a race.
How many ways can 10 people finish a race?
7! There are
720 different outcomes possible
in the race.
How many orders of finish are possible in a 7 horse race?
There are 7*6*5=
210 total ways
in which the 7 horses can come in 1st, 2nd, and 3rd.
How many ways can 5 students line up for a picture?
So the total number of different orderings for the 1st, 2nd and 3rd people combined would be 5*4*3 =
60
.
How many ways can 6 runners finish in 1st 2nd and 3rd place?
This gives us a total of
60 different possible ways
that the runners can come in 1st, 2nd, and 3rd place, assuming no ties.
How many ways can the top 3 winners be selected?
There are
455 ways
the three winners are to be chosen.
How many ways can 5 keys be placed on a key ring?
There are
24 ways
to arrange 5 keys in a keychain.
How many ways can you choose first second and third prize winners of 10 people are eligible?
7! There are
720 different outcomes
possible in the race.
How many different ways are there to rank 7 horses in a horse race?
There are 7*6*5=
210 total ways
in which the 7 horses can come in 1st, 2nd, and 3rd.
How many different ways can 7 cross country runners place in first second and third place?
Therefore, for first and second place, there are 8 x 7 = 56 possibilities. For each one of these, there are 6 possibilities for third place. Therefore, for first, second and third place, there are 56 x 6 =
336 possibilities
“.
How many ways can gold silver and bronze medals be awarded for a race run by 7 people?
In how many different ways can the gold, silver and bronze medals be awarded? Using the Basic Counting Rule, there are 8 choices for the gold medal winner, 7 remaining choices for the silver, and 6 for the bronze, so there are 8 · 7 · 6 =
336 ways
the three medals can be awarded to the 8 runners.
How many ways can 5 persons be seated at a round table?
In how many different ways can five people be seated at a circular table? So the answer is
24
.
How many ways can 5 persons line up to a counter?
In this case it would be the same as ordering people on a line. However if rotation symmetry is taken into account, there are five ways for people to sit at the table which are just rotations of each other. So using symmetry the answer is
24
. Thank you in advance for any explanations!
