Waste less time on Facebook — follow Brilliant.
×

Permutation and Combination

Find the number of ways of permuting the numbers 1,2,3,......upto n . So that they are first increasing and then decreasing ....

Note by Arijit Banerjee
4 years, 2 months ago

No vote yet
2 votes

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

Say, the position of \(n\) is \(k^{th}\) from beginning.

\(k-1\) numbers would be in left of\(n\), and \(n - k\) numbers would be to its right, Select \(k-1\) numbers in the left in\({{n-1} \choose {k-1}}\) ways and arrange them in one order(increasing). Now the others would automatically be arranged in right of \(n\) in descending order in \(1\) way.

Hence , we conclude that :

No. of ways =\(\displaystyle \sum_{k = 2}^{n - 1} {{n-1} \choose {k-1}} = \boxed{2^{n-1} - 2}\)

Jatin Yadav - 4 years, 2 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...