3 Math questions HELP!!!

Test Preparation SAT Preparation
1

<p>Q1. A bakery sells 4 different types of bread. How many combinations of 3 different types of bread can a customer buy from this bakery? </p>

<p>Answer: 4</p>

<p>How do you go about doing this?</p>

<p>Q2. The digits 1, 2, 3 and 4 are to be arranged randomly to make a positive four-digit integer. What is the probability that the digits 1, 2, and 3 will be directly next to each other, in that order, from left to right?</p>

<p>Answer: 1/12</p>

<p>How do you go about doing this?</p>

<p>Q3. Each student in a group of 30 students studies German, Italian, or both. The total number studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?</p>

<p>Answer: 6</p>

<p>How do you go about doing this?</p>

<p>Thanks everyone for their time. I greatly appreciate it!</p>

2

<p>1) Its a permutations and combinations question. 4C3=4!/3!=4
2)There are 4 places that are to be filled with the given digits. for 1,2,3 to be next to each other in that order,you have two ways of doing it (1234) or (4123),ie 2 ways.
Total no. of integers that can be formed=use permutations=4!=24
ans=2/24=1/12.
I would have typed more,but im currently having dinner.</p>