Combination Questions and Answers

Combination Questions

Formula

Definition of Combination

The combination is explained as selecting r series which can be finished out of all n events. It is signified by nCr that sequentially is equivalent to n!/r!(n-r)! Combinations are said to be as the littered sequence of numbers of set elements. For instance, given the set of alphabets {a,b,c}{a,b,c}, the combinations of size 2 (take 2 essentials from the group) are {a,b}{a,b}, {a,c}{a,c}, as well as {b,c}{b,c}. It is important to know that the sequence of the series is not a matter here as {b,a}{b,a} is deliberated similar as {a,b}{a,b}.

Rules

  • We use combinations if an issue arise for the number of tricks of choosing things along with the series of choice is not to be considered.
  • The values of the given combinations of n factors, reserved r at a time is: nCr = n!/(r!)(n-r!)= n (n-1)(n-2)…to r factors / r!
  • While solving combinations, when n = r, the value of combinations is constantly equal to 1.

Question 1

Time: 00:00:00
A man has seven blue marbles and three white marbles. He randomly takes out three marbles. Find the ways in which three marbles are of the same color are selected?

41

41

36

36

91

91

120

120

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Question 2

Time: 00:00:00
A team has 12 players. The ways in which:

(a)  6 players can be selected to start the game?

(b)  3 starting guards?

924 and 220

924 and 220

1011 ans 120

1011 ans 120

950 and 350

950 and 350

550 and 150

550 and 150

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Question 3

Time: 00:00:00
In a group, there are 15 boys and 25 girls. Four players are chosen randomly. The ways in which 3 girls and 1 boy are chosen is:

31250

31250

32200

32200

34500

34500

None of the above

None of the above

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Question 4

Time: 00:00:00
In a school team, there are 14 boys and 9 girls. A new team has to be formed for the inter-school tournament. To form a new team comprising of five students are to be selected such that there are at least 3 boys in the new team. Find the total ways in which it can be done?

24115

24115

24151

24151

21415

21415

25411

25411

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Question 5

Time: 00:00:00
Find the ways in which a group, containing 4 men and 5 women, which can be made from 9 men and 10 women?

12367

12367

38152

38152

31752

31752

37500

37500

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Question 6

Time: 00:00:00
There are 4 boys and 5 girls in a squad. The trainer wants to select a group of 2 boys and 2 girls. How many diverse groups can be made from the team?

70

70

60

60

75

75

88

88

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Question 7

Time: 00:00:00
In a bag, there are 2 pink beads, 3 black beads, and 4 red beads. Calculate the number of ways one can draw 3 beads from the bag, such that at least one out of the three beads is a black bead?

24

24

32

32

64

64

144

144

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Question 8

Time: 00:00:00
In a club, there are 12 men and 9 women. To form a new team of eight people the leader wants at least 4 men in the new team. Find the ways in which it can be done?

16300

16300

12300

12300

163926

163926

15125

15125

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Question 9

Time: 00:00:00
In a basket, there are 2 oranges, 3 apples, and 4 bananas. In how many ways can a person draw 3 fruits from the basket, such that at least two out of the three fruits are bananas?

34

34

72

72

54

54

60

60

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Question 10

Time: 00:00:00
Amongst 6 boys and 4 girls, a new team has to be formed comprising of four people. In how many ways the team can be formed such that at least one girl is there?

195

195

200

200

105

105

150

150

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Question 11

Time: 00:00:00
What are the possible ways one can make a group of 5 males and 2 females from 7 males and 3 females?

63

63

36

36

42

42

24

24

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Question 12

Time: 00:00:00
From a group of 10 American and 8 African people, six girls are to be shortlisted. Find the possible outcomes in which they can be shortlisted, such that there are at least three African girls.

8558

8558

8568

8568

8665

8665

8500

8500

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Question 13

Time: 00:00:00
There was total of ten flavors in an ice-cream parlor. If one can try three scoops, find the ways in which one can try?

360

360

220

220

120

120

720

720