Question

There are 20 identical sticks lined up in a row occupying 20 distinct places as follows: $|1| \|||||||||||||||||||$ Six of them are to be chosen. (a) How many choices are there? (b) How many choices are there if no two of the chosen sticks can be consecutive? (c) How many choices are there if there must be at least two sticks between each pair of chosen sticks?

          There are 20 identical sticks lined up in a row occupying 20 distinct places as follows:
$|1| \|||||||||||||||||||$
Six of them are to be chosen.
(a) How many choices are there?
(b) How many choices are there if no two of the chosen sticks can be consecutive?
(c) How many choices are there if there must be at least two sticks between each pair of chosen sticks?

Added by Cheryl N.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Madhur L

08/17/2023

Step 1

This is a simple combination problem, and the number of ways to do this is given by the binomial coefficient: $\binom{20}{6} = \frac{20!}{6!(20-6)!} = \frac{20!}{6!14!} = 38,760$ So there are $\boxed{38,760}$ ways to choose 6 sticks out of 20. Show more…

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There are 20 identical sticks lined up in a row occupying 20 distinct places as follows: $|1| \|||||||||||||||||||$ Six of them are to be chosen. (a) How many choices are there? (b) How many choices are there if no two of the chosen sticks can be consecutive? (c) How many choices are there if there must be at least two sticks between each pair of chosen sticks?