Two teams are to play a series of 5 matches between them. A match ends in a win or loss or draw for a team. A number of people forecast the result of each match and no two people make the same forecast for the series of matches. The smallest group of people in which one person forecasts correctly for all the matches will contain n people, where n is :


Correct option is


Grope of people ≡ no. of different forecasts that can be done.

3 kinds of forecasts ≡ win, loss or draw

No. of ways

Hence n = 243



How many integral solutions are there to the system of equations

x1 + x2 + x3 + x4 + x5 = 20 and x1 + x2 + x3 = 5 when xk ≥ 0?


There are n points in a plane of which no three are in a straight line except ‘m’ which are all in a straight line. Then the number of different quadrilaterals, that can be formed with the given points as vertices, is :


A father with 8 children takes 3 at a time go to the zoological Garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is :


The number of divisors a number 38808 can have, excluding 1 and the number itself is :


In a class tournament when the participants were to play one game with another, two class players fell ill, having played 3 games each (not played between them). If the total number of games played is 84, the number of participants at the beginning was:


The number of distinct rational numbers x such that 0 < x < 1 and p/q, where p, q ∈ {1, 2, 3, 4, 5, 6}, is:


Let be the set of 4-digit numbers a1a2a3a4 where a1 > a2 > a3 > a2 then (A) is equal to :


The numbers of number of 9 different nonzero digits such that all the digits in the first four places are less than the digit in the middle and all the digits in the last four places are greater than that in the middle is :


Ten persons, amongst whom are A, B and C are to speak at function. Find number of ways in which it can be done if A wants to speak before B, andB wants to speak before C?


Let 1 ≤ m <  ≤ p. The number of subsets of the set A = {1, 2, 3, …,p} having mn, as the least and the greatest elements respectively, is :