In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together
10080
4989600
120960
None of these
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1
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How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together.
Solution 
2
Discuss

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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3
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If ^{18}C_{r }= ^{18}C_{r+2 }; find ^{r}C_{5}.
Solution 
4
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The value of ^{75}P_{2}
Solution 
5
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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 
6
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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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7
Discuss

The number of circles that can be drawn out of 10 points of which 7 are collinear is
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8
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One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is not a face card (Jack, Queen and King only)?
Solution 
9
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Three unbiased coins are tossed. What is the probability of getting at most two heads ?
Solution 
10
Discuss

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)=3/2P(A) and P(C)=1/2P(B), then P(A∪C)=
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