How many ways can Patricia choose 4 pizza toppings from a menu of 8 toppings if each topping can only be chosen once

 70

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Explanation:

Consider we have four slots A, B, C, D.

We have 8 choices for slot A, 7 for B, 6 for C, and 5 for D.

We count down because each time we can't reuse whatever topping was picked earlier.

Multiplying out those values gives: 8*7*6*5 = 1680

There are 1680 permutations. This would be the answer if order mattered, but it doesn't matter.

Since order doesn't matter, we have to divide by 4! = 4*3*2*1 = 24. This is the number of ways to arrange any group of 4 items.

We get 1680/24 = 70 as the final answer

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Another way to get the answer is to apply the nCr combination formula

with n = 8 and r = 4.

Another alternative is to use Pascal's Triangle. You would look in the row that starts with 1,8,... and count out 5 slots (because r starts at r = 0) to arrive at 70.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

answer: the value of x is 7cm

step-by-step explanation: