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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.
Ryan's gym membership costs him $390 per year. He pays this within twelve equal installments a year. How much is every installment? To ?nd out each installment, the total yearl
If arg (a/b) = pi/2, then find the value of ((a+b)/(a-b)) where a,b are complex numbers. Ans) Arg (a/b) =Pi/2 Tan-1 (a/b)= Pi/2 A/B = tanP/2 ,therefore a/b=infinity.
The scores of students taking the ACT college entrance examination are normally distributed with a mean m = 20.1 and a standard deviation s = 5.8. A single student is selected a
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prove that 0!=1
Trig Substitutions - Integration techniques As we have completed in the last couple of sections, now let's start off with a couple of integrals that we should previously be
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We're here going to take a brief detour and notice solutions to non-constant coefficient, second order differential equations of the form. p (t) y′′ + q (t ) y′ + r (t ) y = 0
A shuttlecock used for playing badminton has the shape of a frustum of a Cone mounted on a hemisphere. The external diameters of the frustum are 5 cm and 2 cm, and the height of t
?[1,99] x^5+2x^4+x^3+5x^2+6x+2÷x^2+2x
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