There are eight boxes of chocolates, each box containing distinct number of chocolates from 1 to 8. In how many ways four of these boxes can be given to four persons (one boxes to each) such that the first person gets more chocolates than each of the three, the second person gets more chocolates than the third as well as the fourth persons and the third person gets more chocolates than fourth person?
All the boxes contain distinct number of chocolates.
For each combination of 4 out of 8 boxes, the box with the greatest number has to be given to the first person, the box with the second highest to the second person and so on.
The number of ways of giving 4 boxes to the 4 person is, 8C4 = 70
In how many ways can seven friends be seated in a row having 35 seats, such that no two friends occupy adjacent seats?
First let us consider the 28 unoccupied seats.
They create 29 slots - one on the left of each seat and one on the right of the last one.
We can place the 7 friends in any of these 29 slots i.e. 29P7 ways.
How many ways can 10 letters be posted in 5 post boxes, if each of the post boxes can take more than 10 letters?
Each of the 10 letters can be posted in any of the 5 boxes.
So, the first letter has 5 options, so does the second letter and so on and so forth for all of the 10 letters.
i.e.5 × 5 × 5 × . . . . × 5 (up-to 10 times).
In a hockey championship, there are 153 matches played. Every two team played one match with each other. The number of teams participating in the championship is:
Let there were x teams participating in the games, then total number of matches,
nC2 = 153
On solving we get,
⇒ n = −17 and n =18
It cannot be negative so,
n = 18 is the answer.
A box contains 10 balls out of which 3 are red and rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?