A baseball team has 15 field players and 10 pitchers. Each field player can take any of the 8 non-pitching positions. What is the number of possible starting lineup (8 field player 1 pitcher)

If order matters: 2,594,592,000 ways.

If order does not matter:  64,350 ways

Step-by-step explanation:

Assuming that the order matters when picking the non-pitching positions (since they are different positions), the number of possible different starting lineups is given by the permutation of picking 8 players out of 15, multiplied by 10 (pick one out of 10 pitchers):

Now if the order of the field players is not important, the number of possible starting lineups is given by the combination of picking 8 players out 15, multiplied by 10:

Therefore, the number of ways to pick the starting lineup is:

If order matters: 2,594,592,000 ways.

If order does not matter:  64,350 ways

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.