ACT Math : How to find the greatest or least number of combinations
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Example Questions
Example Question #642 : Arithmetic
A university can send 3 track athletes and 2 field athletes to an upcoming sports event. The university has 14 track athletes and 10 field athletes who qualify. How many different teams can be chosen to attend the sports event?
10,080
64,800
140
16,380
840
16,380
The number of different teams that could be chosen is C(14, 3) × C(10, 2) = 16,380.
Example Question #643 : Arithmetic
The menu above is from Lena’s Italian Kitchen. If you are going there for dinner, how many different combinations of a meal and a salad are there?
15
5
10
20
25
20
Combinations = # first option * # second option
= # meals * # salads
= 5 * 4 = 20
Example Question #11 : How To Find The Greatest Or Least Number Of Combinations
A student is taking a test consisting of six questions. It is a multiple choice test and each question has four answers labelled A, B, C, and D. How many ways can the student answer all six questions if he does not choose the same answer for any two consecutive questions?
100
324
625
972
30
972
the student has four choices for the first question, but only three choices for each of the remaining questions since he does not choose answers with the same letter twice in a row. From the multiplicative counting principle, there are 4 × 3 × 3 × 3 × 3 x 3 = 972 ways Steve can answer the six questions.
Example Question #11 : Permutation / Combination
Ashley is modeling a new mix-and-match clothing line. Her stylist has selected 5 tops, 3 skirts, and 4 jackets for her photo shoot. Assuming that an outfit consists of one top, one skirt, and one jacket, how many outfits can Ashley create for the photo shoot?
60
20
45
30
12
60
In order to calculate the total possible number of combinations, we must multiply the number of possibilities for each piece by one another.
Example Question #11 : Permutation / Combination
In how many ways can the seven members of a students’ council pose in a line for a yearbook photograph if the chair and vice-chair must be side by side?
First find the number of arrangements in which the chair and vice-chair are together. Consider the chair and vice-chair as a unit. This pair as one unit can be arranged with the remaining five members in 
Therefore, there is a total of 2 * 720 = 1440 ways in which the chair and vice-chair are together.
Example Question #1723 : Act Math
Sally is putting on jewelry and has decided to wear one necklace, one pair of earrings, and one ring. Her jewelry collection is listed below. How many different combinations of jewelry can she wear?
|
Necklace |
Earrings |
Ring |
|
short |
studs |
gold |
|
long |
hoops |
silver |
|
|
dangling |
|
3
36
18
7
12
12
To find the number of different combinations, we must use the fundamental counting principal to multiply the number of options in each category together:
(2)(3)(2) = 12
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