6 different coloured balls are there. How many indications can be shown by using any quantity of balls at a time?
Answers
Answer:
Total ways = 1956
Step-by-step explanation:
If we consider that arrangement of ball matters here then we have to use permutation formula and if arrangement or order of selected ball does not matter then we have to use formula for combination.
Here I am finding the solution by using the permutation.
Case.1
If we use single ball at a time then
There are 6 different ways because 6P1 = 6!/(6-1)! = 6
Case.2
If we use 2 balls at the time then
6P2 = 6!/(6−2)!
= 30
Case.3
If we use 3 balls at the time then
6P3 = 6!/(6−3)!
= 120
Case.4
If we use 4 balls at the time then
6P4 = 6!/(6−4)!
= 360
Case.5
If we use 5 balls at the time then
6P5 = 6!/(6−5)!
= 720
Case.6
If we use 6 balls at the time then
6P6 = 6!/(6−6)!
= 720
Thus
Total ways = 720 + 720 + 360 + 120 + 30 + 6 = 1956
Total ways = 1956