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1) In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?A) 209 B) 208 C) 210 D) 215
Answer & Explanation
Answer: 209 (We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4) = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2) =209
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2) In how many ways a committee, consisting of 4 men and 4 women can be formed from 8 men and 10 women?A) 12000 B) 15200 C) 15000 D) 14700
3) A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?A) 50 B) 56 C) 64 D) 60
Answer & Explanation
Answer: 64 (We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
= (45 + 18 + 1)
= 64.)
4) In how many ways can a group of 4 men and 2 women be made out of a total of 7 men and 3 women?A) 108 B) 105 C) 110 D) 106
Answer & Explanation
Answer: 105 (Required number of ways = (7C4 x 3C2) = (7C3 x 3C1) = 35 *3 = 105)
5) In how many ways can the letters of the word 'WALL be arranged?A) 14 B) 16 C) 20 D) 12
Answer & Explanation
Answer: 12 (The word WALL contains 4 letters, namely 2L,1W, 1A
Required number of ways = 4!/(1!)(2!)(1!) = 12.
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