How many orders of faces are possible when a standard die is rolled four times?
A. 16
B. 24
C. 1296
D. 4096
Which of the following is equivalent
A. _{101}P_{98} ?
B. 101 \times 100 \times 99 \times 98
C. \displaystyle
\frac{101!}{98!}
D. \displaystyle
\frac{101!}{3!}
When flipping a coin five times, what is the probability that heads turns up every time?
A. \displaystyle
\frac{1}{32}
B. \displaystyle
\frac{5}{32}
C. \displaystyle
\frac{1}{10}
D. \displaystyle
\frac{1}{25}
Which of the following is not defined? Explain your reasoning.
\displaystyle
_{12}P_8
\displaystyle
_{9}P_{10}
\displaystyle
_{7}P_{0}
\displaystyle
_{100}P_{100}
Rosa is getting dressed and has decided that her shirt, pants, and socks are not to be the same colour. She has red, green, black, and blue of each.
a) Draw a tree diagram illustrating her choices.
b) How many choices does she have if she starts with a red pair of pants?
A hockey team has four left wingers, three right wingers, four centres, three left defence, four right defence, and two goalies. To create a starting lineup, a coach needs one player in each position. In how many ways could the starting lineup be chosen?
How many ways are there to assign five different roles in a play to the 12 members of a drama club?
There are three Canadians in the finals at a ski competition. Assuming all eight competitors are equally likely to win. what is the probability that the three Canadians will win gold, silver, and bronze?
a) How many arrangements are there of the letters in the word COMPUTER?
b) How many of them begin with a consonant?
In how many ways could the 11 members of a soccer team line up if the captain and assistant captain must remain apart?
There are 25 men and 20 women who belong to a club. An executive panel consisting of a president. vice president. secretary. and treasurer is being chosen.
a) In how many ways could the executive panel be chosen with no restrictions?
b) In how many ways could the executive panel be chosen if it must include at least one woman and one man?
c) In how many ways could the executive panel be chosen if the president and vice president must have different genders?
Four letters are randomly selected from the alphabet. What is the probability that they are A, B, C, and D, in that order,
a) if repetition is permitted?
b) if repetition is not permitted?
Ten people each randomly select a number between 1 and 20. What is the probability that at least two of them select the same number?
To determine who should be the first dealer in a card game. one card is dealt to each of five players. The player with the card of the highest denomination gets to deal first.
a) How many different results are possible when dealing to the five players?
b) In how many ways could all players receive cards of different denominations?
c) What is the probability that four players receive cards of the same denomination?
d) How would the solution to part c) change if players each chose a card from a full deck instead of being dealt one?