Basic Counting Techniques in Probability

A luggage lock opens with the correct four-letter code. Each wheel rotates through the letters A to L. How many different four-letter codes are possible?

• 256

• 20736

• 48

• 16777216

The locks on a briefcase open with the correct six-digit code. Each wheel rotates through the digits 0 to 9.

a) How many different six-digit codes are possible?

b) What percent of these codes have no repeated digits?

• a) 1,000,000 codes b) 151200%

• a) 1,000,000 codes b) 15.12%

• a) 151200 codes b) 10%

• a) 531441 codes b) 11.38%

How many numbers are there from 100 to 199 that do not have any repeated digits?

• 72

• 68

• 75

• Not enough information to determine

Three quarters are flipped simultaneously. How many ways can two coins land heads and one coin lands tails? (a tree diagram will help)

• 2

• 3

• 4

• 5

The dinner special at a restaurant offers you a choice of 7 entrees, 3 salads, 8 drinks, and 5 desserts. How many different meals are possible if you choose one item from each category?

• 840

• 23

• 19320

• 863

Five students from a class of 20 have been chosen to be the starting team. The starting team includes a point guard, a shooting guard, a small forward, a power forward, and a centre. How many arrangements of the starting team are possible if Mildred and Natasha must play the guard positions?

• 12

• 9792

• 1744200

• 120

Which expression correctly describes the theoretical probability, P(A), where n(A) is the number of outcomes favourable to event A and n(T) is the total number of outcomes in the sample space, T, in the experiment?

Given the following probabilities, which event is most likely to occur?

Julie draws a card at random from a standard deck of 52 playing cards. Determine the odds in favour of the card being a heart.

Tia notices that yogurt is on sale at a local grocery store. The last eight times that yogurt was on sale, it was available only three times. Determine the odds against yogurt being available this time.

• 3:8

• 3:5

• 5:3

• 8:3