FREE! Click here to Join FunTrivia. Thousands of games, quizzes, and lots more!
Fun Trivia
Home: Questions and Answers Forum
Answers to 100,000 Fascinating Questions
Welcome to FunTrivia's Question & Answer forum!

Search All Questions


Please cite any factual claims with citation links or references from authoritative sources. Editors continuously recheck submissions and claims.

Archived Questions

Goto Qn #


In the lottery there are 49 balls. How many different combinations are there of a drawing of 6 balls?

Question #51851. Asked by hvj.
Last updated May 21 2024.

Related Trivia Topics: World  
peasypod
Answer has 10 votes
Currently Best Answer
peasypod
21 year member
3273 replies

Answer has 10 votes.

Currently voted the best answer.
Choosing 6 objects from 49 possibilities gives....
49!/(49-6)!6! = 13,983,816 combinations

where the "factorial" is defined by
x! = x*(x-1)*(x-2)*.....*3*2*1

For a calculator of combinations see link http://www.calculatorsoup.com/calculators/discretemathematics/combinations.php

Response last updated by nautilator on Aug 21 2016.
Oct 21 2004, 2:14 AM
gmackematix
Answer has 10 votes
gmackematix
21 year member
3206 replies

Answer has 10 votes.
The question asked how many "different combinaions" there were. Peasy has the correct answer, now let's try and put it as clearly as possible.

For each of the 49 ways to pick the first ball, there are 48 ways to pick the second, leaving 47 ways to pick the third ball and so on. The total number of ways of picking six balls is out is therefore equal to 49x48x47x46x45x44.

However picking 1,2,3,4,5,6 is no different in lottery terms to picking out 6,3,1,4,2,5 or 5,1,3,2,6,4. So above we have counted every group of six balls a number of times. This number is the number of different ways of arranging six balls in order. If we take 10,15,20,25,30,35 as an example. In any arrangement 10 must come first, second, third, fourth, fifth or sixth. This leaves five places for 15, four for 20 and so on. So the number of ways six balls can be arranged is 6x5x4x3x2x1 = 720. As each group of six balls in the answer above we can divide by 720.

A calculator shows that 49x48x47x46x45x44/720 = 13,983,816.


Response last updated by gtho4 on May 21 2024.
Oct 21 2004, 5:21 PM
free email trivia FREE! Get a new mixed Fun Trivia quiz each day in your email. It's a fun way to start your day!


arrow Your Email Address:

Sign in or Create Free User ID to participate in the discussion

Related FunTrivia Quizzes

play quiz They Had Four Balls?
( Batting Records)
play quiz Balls
(Thematic Toys)
play quiz New Balls Please
(Tennis Players Mixed)

Return to FunTrivia
"Ask FunTrivia" strives to offer the best answers possible to trivia questions. We ask our submitters to thoroughly research questions and provide sources where possible. Feel free to post corrections or additions. This is server B184.