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Q:

How many ways are there to deal a five-card hand consisting of three eight's and two sevens?

A) 36	B) 72
C) 24	D) 16

Answer & Explanation Answer: C) 24

Explanation:

If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.

The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.

We have 4 eights and 4 sevens.

We want 3 eights and 2 sevens.

C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens)

C(4,3) x C(4,2) = 24

Therefore there are 24 different ways in which to deal the desired hand.

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Q:

A school has scheduled three volleyball games, two soccer games, and four basketball games. You have a ticket allowing you to attend three of the games. In how many ways can you go to two basketball games and one of the other events?

A) 25	B) 30
C) 50	D) 75

Answer & Explanation Answer: B) 30

Explanation:

Since order does not matter it is a combination.

The word AND means multiply.

Given 4 basketball, 3 volleyball, 2 soccer.

We want 2 basketball games and 1 other event. There are 5 choices left.

C(n,r)

C(How many do you have, How many do you want)

C(have 4 basketball, want 2 basketball) x C(have 5 choices left, want 1)

C(4,2) x C(5,1) = (6)(5) = 30

Therefore there are 30 different ways in which you can go to two basketball games and one of the other events.

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Q:

Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

A) 2589860	B) 2598970
C) 2598960	D) 2430803

Answer & Explanation Answer: C) 2598960

Explanation:

When a hand of cards is dealt, the order of the cards does not matter. If you are dealt two kings, it does not matter if the two kings came with the first two cards or the last two cards. Thus cards are combinations. There are 52 cards in a deck and we want to know how many different ways we can put them in groups of five at a time when order does not matter. The combination formula is used.

C(52,5) = 2,598,960

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Q:

How many ways are there to select a subcommittee of 7 members from among a committee of 17?

A) 19000	B) 19448
C) 19821	D) 19340

Answer & Explanation Answer: B) 19448

Explanation:

Since it does not matter what order the committee members are chosen in, the combination formula is used.

Committees are always a combination unless the problem states that someone like a president has higher hierarchy over another person. If the committee is ordered, then it is a permutation.

C(17,7)= 19,448

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Q:

Find the number of ways to take 20 objects and arrange them in groups of 5 at a time where order does not matter.?

A) 57090	B) 15540
C) 15504	D) 23670

Answer & Explanation Answer: C) 15504

Explanation:

${}^{20}C_{5}$ = 15504

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Q:

Find the number of ways to take 4 people and place them in groups of 3 at a time where order does not matter?

A) 4	B) 12
C) 36	D) 16

Answer & Explanation Answer: A) 4

Explanation:

Since order does not matter, use the combination formula

${}^{4}C_{3}$ = 24/6 = 4

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Q:

Find the number of ways to arrange 6 items in groups of 4 at a time where order matters?

A) 720	B) 640
C) 740	D) 360

Answer & Explanation Answer: D) 360

Explanation:

6P4 = 6! / (6-4)! = 360

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Q:

Find the number of ways to arrange 4 people in groups of 3 at a time where order matters?

A) 20	B) 16
C) 24	D) 36

Answer & Explanation Answer: C) 24

Explanation:

P(4,3)= ${}^{4}P_{3}$ = 24

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