Jennifer writes the letters M-O-N-T-A-N-A on cards and then places the cards in a hat. What is the probability of picking an M?
There is a total of 7 letters in "MONTANA." Since only one letter is an M, the probability of picking an M is 1/7.
Jamal writes the letters K-A-N-S-A-S on cards and then places the cards in a hat. What is the probability of picking an S?
There is a total of 7 letters in "KANSAS." Since there are two letters that are S, the probability of picking an S is 2/7.
Jamal writes the letters K-A-N-S-A-S on cards and then places the cards in a hat. What is the probability of picking a vowel?
Out of the 7 letters in "KANSAS," there are two vowels: A and the second A. Therefore, there is a total of 2 vowels.
The probability of picking a vowel is then:
2 (number of vowels) / 7 (total number of letters) = 2/7
5. You and 4 friends go to a concert. In how many different ways can you sit in the assigned
seats?
20
24
48
120
Assuming that each seat is distinct (i.e. one seat is not the same as another), the number of ways you and your four friends can sit in the assigned seats is equal to the number of permutations of 5 objects, which is given by:
5! = 5 x 4 x 3 x 2 x 1 = 120
Therefore, the answer is 120.
14. How many ways can 3 students be chosen from a class of 20 to represent their class at a banquet?
6,840
3,420
1,140
2,280
The number of ways to choose 3 students from a class of 20 is given by the combination formula:
C(20, 3) = 20! / (3! * (20 - 3)!) = 20 x 19 x 18 / (3 x 2 x 1) = 1,140
Therefore, the answer is 1,140.
Simplify ¹⁰P⁴ (1 point)
210
360
5,040
151,200,