My Math Forum Combo and permutations questions with better pictures

 October 6th, 2014, 02:14 PM #1 Newbie   Joined: Sep 2014 Posts: 25 Thanks: 0 Combo and permutations questions with better pictures Please help me with 1, 3, 5, 6 Thank you
 October 7th, 2014, 01:21 PM #2 Global Moderator   Joined: May 2007 Posts: 6,821 Thanks: 723 Picture is very blurred!
October 7th, 2014, 08:21 PM   #3
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Joined: Jul 2014
From: भारत

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Having a look at the first question suck up a lot of my time !
Also, all questions (1,3,5 and 6) are related to permutations and combinations.
So, I am solving the fifth one. Taking inspiration from this solution, solve the rest.
Quote:
 How many ways can a committee of 3 be selected from a club with 12 members?
this is a combination problem
involving "CHOOSING"
where order doesn't matter

the formula for choosing k objects from n objects is
$\displaystyle ^{n}{_{C_k}} = \frac{n!}{\left( k! \times (n-k)! \right) }$
where n! is called factorial n
& is $\displaystyle n \cdot (n-1) \times (n-2) \times... \times 1$

thus number of ways = $\displaystyle ^{12}{_{C_{3}}} = \frac{12!}{( 3! \times 9!)}$

$\displaystyle = 12 \times 11 \times \frac{10}{(1 \times 2 \times 3)} = 220$

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