Tip #33 to Get a Top ACT Math Score (page 2)
Arrangement questions ask you how many arrangements of something are possible, such as how many different ways 4 letters can be arranged. Most tests have at least one of these. Arrangement questions seem impossible to many students, but they are easy if you know the steps:
Step 1. Draw a blank for each position.
Step 2. Fill in the # of possibilities to fill each position.
Step 3. Multiply.
Let's look at this question:
- Draw a blank for each position.
- Enter the number of possibilities that can fill each position.
- Multiply the numbers to get the number of arrangements! 4 × 3 × 2 = 24
Correct answer: C
That's the way to do 95% of ACT arrangement questions. There is only one trick that the ACT tries. If a question is about teams of two or pairs or specifically points out repeated pairs, then divide your answer by 2.
Here's an example: There are 12 children in a class. Two will be chosen as a team to go and hide for a game. How many such teams of two children are possible?
Draw two blanks for the two children on the team. Fill in the number of possibilities for each blank. Multiply the numbers: 12 × 11=132. Normally you'd be done, but here we have one final step: we divide the answer by 2. For this team of two kids, it doesn't matter if it's Jimmy and Jill or Jill and Jimmy, so there are exactly twice as many answers as there should be. This rule works for any team of two. (If the ACT used a team of three, then we would divide by the number 6, but usually they use teams of two and we divide by the number 2.)
- For a fund raiser, the meditation club is selling T-shirts with a choice of two slogans, "See clearly" or "Nonattachment." Each shirt is available in small, medium, or large. How many different types of shirts are available?
- Five actors are being cast to fill five roles. If each actor plays only one role, how many different arrangements of actors in the five roles are possible?
- At the build-your-own-burrito bar you can choose chicken, beef, or shrimp. You can include no vegetable, spinach, or sautéed zucchini; and you can top it with mild, medium, hot, or killer salsa. How many different burritos can be ordered?
- Kyle will write 3 of the symbols shown below on a banner. How many such arrangements are possible?
- 3 ♣ ♥ Φ ψ
- Of the six members of the girls tennis club, two will compete as the doubles team. How many different such teams of two girls are possible?
- E Draw a blank for each option. Then write in the number of possibilities that can fill each option. There are 2 slogan options and 3 size options, so 2 × 3 = 6. Notice that this question is simple enough to do without the strategy; you could just picture shirts in piles, like at Old Navy, with two different slogans available in S, M, and L, making 6 piles.
- J Draw a blank for each role that needs to be filled by an actor. Then write in the number of actors who can fill the role. Remember that each actor can play only one role, so once someone is assigned, that person can't be used again. Then multiply.
- D Draw a blank for each spot at the burrito bar. Then write in the number of possibilities that can fill each slot. There are 3 options for meat, 3 options for vegetables, and 4 options for salsas, so 3 × 3 × 4 = 36.
- K Draw a blank for each spot on the banner. Fill in the number of possible symbols that can go in each spot. Notice that the three symbols must be different, since the question states that Kyle will use three of the symbols. Therefore, they cannot be reused, and we have 5 × 4 × 3 = 60.
- C Draw a blank for each member of the doubles team. Write in the number of possible girls who can fill each slot; remember that once someone is assigned a position, she cannot also play another position. Then multiply. This question has one extra step, since this is a team of two, and it does not matter if it's Jenny and Jill or Jill and Jenny. So we divide our answer by 2 since we will have double-counted each duo. 6 × 5 = 30 ÷ 2 = 15.
5 × 4 × 3 × 2 × 1 = 120.
Go to: Tip #34
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