Simulation · Maths · Class 11
Selections, and the orders inside them
From the lesson Combinations in Permutations and Combinations. Change the values and watch what happens.
Selections, and the orders inside themMaths · Class 11
The idea behind it
NCERT §6.4
- A combination is a selection in which order does not matter: choosing A and B is the same as choosing B and A.
- nCr = n!/(r!(n − r)!), for 0 ≤ r ≤ n. It links to permutations by nPr = nCr × r!, because each selection of r objects can be put in order in r! ways.
- Relay: the team of 4 from 7 sprinters can be picked in 7C4 = 35 ways. Each team has 4! = 24 running orders, and 35 × 24 = 840 = 7P4.
- Handshakes: 10 house captains each shake hands once with every other: 10C2 = 45 handshakes.
- Points on a circle: 8 points give 8C2 = 28 chords and 8C3 = 56 triangles, since no three of them lie on a line.
- nC0 = 1 and nCn = 1: there is one way to choose nothing and one way to choose everything. A committee of 3 from 6 volunteers can be picked in 6C3 = 20 ways.