Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

You are not logged in.

## #1 2018-03-09 07:21:39

Hannibal lecter
Member
Registered: 2016-02-11
Posts: 225
Website

### how many permutation the following set has

Hi, how many permutation the set has X= ={1,1,2,2,6}

int  repetitions and without  repetitions

Wisdom is a tree which grows in the heart and fruits on the tongue

Offline

## #2 2018-03-09 22:01:58

bob bundy
Registered: 2010-06-20
Posts: 8,417

### Re: how many permutation the following set has

hi Hannibal lecter

If repetitions are allowed:

If the five numbers were all different it would be 5! = 5x4x3x2x1.

But we have repeated 1s.  You couldn't tell the difference between 16122 and 16122 where I have swapped the 1s around.  So very possibility gets counted twice because of the repeated 1s and similarly the 2s.  S we need to calculate 5! ÷ 2 ÷ 2

If repetitions are not allowed the set is effectively reduced to {1,2,6} so it's just 3! = 3x2x1.

126, 162, 261, 216, 612, 621.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

Offline