+31 1.There are 20 people in my club. 8 of them are left-handed. 15 of them like jazz music. 2 of them are right handed and dislike jazz music. How many club members are left handed and like jazz music?
2.Mr.Stewarts class has 16 boys, and 22 of his studentsbring thier calculators to class. If 13 of thestudentswith calculators are girls, then how many boys did not bring thier calculators?
3.You have 5 shirts, 6 pairs of pants, and 8 hats. How many outfits can you make consiting with 1 shirt, 1 pair of pants, and 1 hat?
4. How many 3-letter combinations can be formed if the second letter must be a vowel(A,E,I,O,or U), and the third letter must be different from the first letter?
5.The local theater has one ticket window. In how many ways can 6 people line upto buy a ticket?
6.In how many ways can you order 7 differnt colored hats in a row?
7. Our basketball team has 12 members, each of whom can play any position. In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting foward, a point guard, and a shooting guard?
+128707 4. How many 3-letter combinations can be formed if the second letter must be a vowel(A,E,I,O,or U), and the third letter must be different from the first letter?
The frist letter can be selected in 26 ways
The second letter can be selected in 5 ways
And since the third letter must be different from the first, we have 25 choices left for it
So.....the total number = 26 * 5 * 25 = 26 * 125 = 3250 combinations
+128707 1.There are 20 people in my club. 8 of them are left-handed. 15 of them like jazz music. 2 of them are right handed and dislike jazz music. How many club members are left handed and like jazz music?
If 8 are left-handed, then 20 - 8 = 12 must be right-handed........assuming that all the right-handed people have a preference for either liking or disliking jazz music, then 12 - 2 = 10 of the right-handed people must like it.......which means that 15 - 10 = 5 left-handed people like jazz music
+128707 2.Mr.Stewarts class has 16 boys, and 22 of his studentsbring thier calculators to class. If 13 of thestudentswith calculators are girls, then how many boys did not bring thier calculators?
The number of boys who brought their calculators to class must be 22 - 13 = 9
And if there are 16 boys, then 16 - 9 = 7 did not bring their calculators
+128707 3.You have 5 shirts, 6 pairs of pants, and 8 hats. How many outfits can you make consiting with 1 shirt, 1 pair of pants, and 1 hat?
We want to choose 1 of 5 shirts = 5 choices
And 1 of 6 pairs of pants = 6 choices
And 1 of 8 hats = 8 choices
So....the total number of different outfits = 5 * 6 * 8 = 30 * 8 = 240
+128707 4. How many 3-letter combinations can be formed if the second letter must be a vowel(A,E,I,O,or U), and the third letter must be different from the first letter?
The frist letter can be selected in 26 ways
The second letter can be selected in 5 ways
And since the third letter must be different from the first, we have 25 choices left for it
So.....the total number = 26 * 5 * 25 = 26 * 125 = 3250 combinations
+128707 5.The local theater has one ticket window. In how many ways can 6 people line upto buy a ticket?
The total number of ways = 6! = 720
6.In how many ways can you order 7 different colored hats in a row?
This is similar to (5).......7! = 5040 ways
7. Our basketball team has 12 members, each of whom can play any position. In how many ways can we choose a starting lineup consisting of a center, a power forward, a shooting foward, a point guard, and a shooting guard?
We have 12 ways to choose the center, 11 to choose a power forward, 10 to choose a shooting forward, etc........so 12* 11 * 10 * 9 * 8 = P(12,5) = 95040 ways
