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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:

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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Q:

If repetition of the digits is allowed, then the number of even natural numbers having three digits is :

A) 550	B) 450
C) 500	D) 540

Answer & Explanation Answer: B) 450

Explanation:

In a 3 digit number one’s place can be filled in 5 different ways with (0,2,4,6,8)

10’s place can be filled in 10 different ways

100’s place can be filled in 9 different ways

There fore total number of ways = 5X10X9 = 450

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Q:

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word ‘SACHIN’ appears at serial number :

A) 601	B) 600
C) 603	D) 602

Answer & Explanation Answer: A) 601

Explanation:

If the word started with the letter A then the remaining 5 positions can be filled in 5! Ways.

If it started with c then the remaining 5 positions can be filled in 5! Ways.Similarly if it started with H,I,N the remaining 5 positions can be filled in 5! Ways.

If it started with S then the remaining position can be filled with A,C,H,I,N in alphabetical order as on dictionary.

The required word SACHIN can be obtained after the 5X5!=600 Ways i.e. SACHIN is the 601th letter.

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