PROBLEM LINK:
Author: RAVIT SINGH MALIK
Editorialist: RAVIT SINGH MALIK
DIFFICULTY:
EASY
PREREQUISITES:
MATHS,NUMBER THEORY
PROBLEM:
Find the number of ways of selecting one or more items from N distinct things.
EXPLANATION:
So, Number of ways of selecting one or more items from N distinct things.
nC0 + nC1 + nC2 + nC3 + ------------- + nCn = 2^n
nC1 + -----------------nCn =2^n - nC0
= 2^n – 1 , [ nC0=1]
FOR example,
you need to find number of ways of selecting one or more items from 5 distinct things.
so,
5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 2^5
5C1 + 5C2 + 5C3 + 5C4 + 5C5 =2^n - 5C0
= 2^5 – 1=31
AUTHOR’S AND TESTER’S SOLUTIONS:
Author’s solution can be found here.