Combination & Probability (2)( Week 42 Evaluation) 1. Alice spent exactly $2.50 for some 23-cent stamps and 15-cent stamps. How many stamps did she buy in total? 2. There are 4 cards with numbers 0, 7, 8, and 9 on them. These 4 cards were put in a box. You are asked to randomly pick up two cards each time to form a two-digit number (Cards are then put back). How many different two-digit numbers can you form? 3. There are 17 socks in a drawer. Among them, 5 are black, 6 are white and 6 are blue. Ben picks one sock from the drawer (without returning it), and it is black. He picks another one (without returning it), and it is white. If he randomly picks the third sock from the drawer, what is the probability that the sock is blue? 4.
If one of the figures above is selected at random, what is the probability that the number of sides in the selected figure will be less than 5? 5. Steve has the following coins in his pocket: 3 pennies, 1 nickel, 3 dimes, 3 quarters, and 3 half-dollars. 11 of these coins are taken out of the pocket and the sum of their values is recorded. How many different sums are possible? 6. There are 12 ways to make 25 cents using the coins (quarters, dimes, nickels, and pennies). How many ways can you make 50 cents using the coins? 7. Two students are needed to volunteer in a public library every day. 4 students signed up for the volunteer position. What is the greatest number of days that can be arranged so that no pair of the students work together more than once? 8. There are 9 cards with numbers 2, 2, 3, 4, 5, 6, 7, 8, and 9 on them. These 9 cards were put in a box. You are asked to randomly pick up two cards each time to form a two-digit number (Cards are then put back). How many different two-digit numbers can you form? 9. 5 different points are chosen on a circle, and chords are drawn connecting every pair of points. No three chords intersect in a single point inside the circle. How many triangles with all the vertices in the interior of the circle are created? 10. In a certain money system, there are 3 types of coins with each values 1 cent, 5 cents, and 10 cents respectively. In how many different ways can you make a 16 cents total? |