There are seven pairs of black shoes and five pairs of white shoes. They are all put into a box and shoes are drawn one at a time. To ensure that at least one pair of black shoes are taken out, what is the number of shoes required to be drawn out?
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1
Discuss

In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
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2
Discuss

If a team of 4 persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least 1 female
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3
Discuss

There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters.
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4
Discuss

A person tosses an unbiased coin. When head turns up, he gets Rs.8 and tail turns up he loses Rs.4. If 3 coins are tossed, what is probability that he gets a profit of Rs.12?
SolutionPerson will get profit of Rs 12 only when there is 2H (Head) and 1T (Tail) H + H + T = 12 8 + 8 + (4) = 12 Total outcome of 2 head and 1 tail = 2^{3} = 8 i.e (T, H, TH, HT, HH, HHT, HTH, THH) Total event with 2H and 1 T is 3 therfore probability = 3/8 
5
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A box contains two white balls, three black balls and four red balls. Balls of the same colour are distinct. The number of ways in which three balls can be drawn from the box if atleast one black ball is to be included in the draw, is
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6
Discuss

If (n + 2)! = 2550 (n!); find ’n’
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7
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A basketball team of 5 players is to be selected from a group of 10 men and 8 women players. A volley ball team of 6 players is to be selected from a group of 8 men and 7 women players. Find the difference in the number of ways in which both the teams are selected, given that each team has only 2 female players.
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8
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12 person are seated at a round table. Number of ways of selecting 2 persons not adjacent to each other is
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9
Discuss

How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
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10
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If A and B are two independent events with P(A) = 3/5 and P(B) = 4/9 , then P(A' ∩ B' ) equals
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