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Shirts numbered consecutively from 1 to 20 are worn by 20 members of a bowling league. While any three of these members are selected to be a team, the league aims to use the sum of their shirt numbers as the code number for the team. Display that if any eight of the 20 are chosen, after that from these eight one may form at least two different teams having similar code number
Ans: While a team containing three persons is selected and number inscribed on the shirt is added, the possible minimum number is (1+ 2 + 3 =) 6 and the maximum number is (18 + 19 + 20 =) 57. So a team of three can have a code number from the possible range of 52 codes from 6 to 57 both inclusive. Now after selecting 8 from 20 members, any three out of 8 can be selected in
8C3 = 56.
Now using the Pigeon Hole principle, let 56 pigeons are placed into 52 holes marked with codes between 6 and 57, then there are at least two teams will be in the same hole, implying that these two teams will have the same code number.
Identify the surface for each of the subsequent equations. (a) r = 5 (b) r 2 + z 2 = 100 (c) z = r Solution (a) In two dimensions we are familiar with that this
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all??
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Solve cos( 4 θ ) = -1 . Solution There actually isn't too much to do along with this problem. However, it is different from all the others done to this point. All the oth
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Suppose that the width of a rectangle is three feet shorter than length and that the perimeter of the rectangle is 86 feet. a) Set up an equation for the perimeter involving on
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If ABC is an obtuse angled triangle, obtuse angled at B and if AD⊥CB Prove that AC 2 =AB 2 + BC 2 +2BCxBD Ans: AC 2 = AD 2 + CD 2 = AD 2 + (BC + BD) 2 = A
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