There are seven pairs of black shoes and five pairs of white...

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?

Course Name: Quantitative Aptitude

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1 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)= 1] 3/13 2] 6/13 3] 7/13 4] 10/13 Solution
10 Discuss	If four dice are thrown together, then what is the probability that the sum of the numbers appearing on them is 25 ? 1] 0 2] 1/2 3] 1 4] 1/1296 Solution
2 Discuss	How many words can be formed from the letters of the word "SIGNATURE" so that vowels always come together. 1] 17280 2] 4320 3] 720 4] 80 Solution
3 Discuss	A, B, C, D and E sit on five chairs all of which are facing north. C will sit only on the leftmost chair and B will not sit anywhere to the left of A. In how many ways they can be seated? 1] 10 2] 18 3] 36 4] 12 Solution
4 Discuss	A five-letter word is to be formed from a group of 5 vowels and 4 consonants, using at least one vowel and at least one consonant. In how many ways the word having a greater number of consonants than vowels can be formed? 1] 40 2] 42 3] 45 4] 52 Solution
5 Discuss	A teacher has to choose the maximum different groups of three students from a total of six students. Of these groups, in how many groups there will be included in a particular student? 1] 12 2] 10 3] 8 4] 6 Solution
6 Discuss	If C(n, 7) = C(n, 5), find n 1] 12 2] 15 3] 18 4] -1 Solution
7 Discuss	How many natural numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million? 1] 496 2] 728 3] 486 4] 1084 Solution
8 Discuss	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 1] 32 2] 64 3] 128 4] None Of These Solution
9 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. 1] 2! x 19! 2] 18! 3] 18! x 2! 4] 19! Solution
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