Which of the problems below is not a permutation? the number of ways 20 people can finish in the first three places in a race. how many different kinds of pizzas can be made with 12 optional toppings. how many ways 15 people can arrange themselves in a straight line. how many ways the top 20 hit songs can be arranged from a selection of 500 current singles.

Permutation is defined as the possible combinations or variation in which a number of things can be ordered or arranged.    

All the examples provided are permutation, except -- How many different kinds of pizzas can be made with 12 optional toppings.  

Other examples are clear examples of permutations. With permutations, order matters.

22 dimes and 9 nickels

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,