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If a password contains exactly 6 letters, how many passwords are possible if letters cannot be used more than once? How many ways can a

  1. If a password contains exactly 6 letters, how many passwords are possible if letters cannot be used more than once?
  2. How many ways can a cook arrange 7 of 10 spice jars on a spice rack?
  3. If I have 9 pieces of luggage, how many ways can I select 3 pieces of luggage for a trip?
  4. A bin contains 10 cards labeled A to J and 20 cards labeled 1 to 20. The cards are shuffled and one card is chosen at random. What is the probability that the card is a letter in the word DIG or an odd number?
  5. If I set up 3 rows of 10 chairs in front of the stage, what expression gives the probability that the seat that is randomly chosen is a front row seat or an aisle seat?
  6. If a pond is freshly stocked with 6 brown trout and 18 lake trout and I catch and release a trout and then catch another trout a while later, what is the probability that I caught a brown trout each time?
  7. If I have 12 brown socks and 6 blue socks in a drawer and it's dark when I pull out a sock and put it on my right foot, and then I pull out another sock and put it on my left foot, what is the probability that I have two brown socks on my feet?

  1. The table shows the results of an experiment in which a 6 sided number cube is rolled several times. If I rolled a 6-sided cube several times, and the data shows the result of my experiment, what is the experimental probability of rolling an even number?
Outcome Frequency
1 3
2 3
3 4
4 1
5 5
6 2

9. If I have a spinner that's divided into 4 quadrants - 1,2,3,4 - and I spin it 8 times, and in those 8 spins, the arrow never lands on 3, should I be concerned that the spinner is unfair? Also if I spin the spinner 500 times, and the arrow lands on 3 a total of 42 times, should I be concerned that the spinner is unfair? How would I determine if these numbers are showing that there is, in fact, something wrong with the spinner?

10. If there are 20 marbles in a bag and if I draw from the bag 1,000 times (with replacement after each draw), and 50% of the time I draw red, and 25% of the time I draw blue and 25% of the time I draw white, how many of the 20 marbles are red, blue, and white? Can I safely say that 10 of them are red, 5 are blue and 5 are white?

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