How to answer a Combinations question

• I
• Biochemgirl2002
In summary, the conversation discusses the process of picking six numbers from a set of 1 to 49 when playing Lotto 649. The total number of ways to do this is determined by the formula n!/r!(n-r)!, which simplifies to (49*48*47*46*45*44)/(6*5*4*3*2*1) or 13,983,816. However, it is important to understand the order of operations in mathematical expressions to avoid confusion and mistakes.
Biochemgirl2002
Question: When playing Lotto 649, you must pick six numbers from the numbers 1, 2, …, 49. In how many ways can you do this?

My attempt

n!/r!(n-r)! = 49!/6!(49-6)!
(49x48x47x46x...x1)/(6x5x4x3x2x1)(43x42x41x40x...x1)

=0.06 .
(edit: i redid the question and just made it (49x48x47x46x45x44)/(6!) and i got 13,983,816. this seems like it could be the right answer but i am still hesitant because I am not sure that is legal to just remove the 43! from the denominator)

this is definitely wrong, since the number should be huge, but I am not sure how to approach the correct answer

I think your formula is missing some parens:

## n! / r! (n-r)! ## which is in fact ##\frac {n!} {r!} (n-r)! ## should be ##\frac {n! } {(r! (n-r)!)} ##

by way of explanation, you choose 6 numbers out of 49 which is 49*48*47*46*45*44 or
49! / (49-6)! and now since the order doesn't matter you divide by 6!

Alright, so if i did the equation

(49*48*47*46*45*44)/(6*5*4*3*2*1) ,
so therefore the answer would be 13,983,816 ?

Just understand the meaning of your formula ie basically learn how to derive it and understand how it works and what its limitations are...

Walk around and amaze your friends by computing probabilities of related events.

The mistake you made here is a common meme among folks studying the order of math operations in fuzzy expressions that's why I added the parens to make it clear.

https://www.insider.com/hard-viral-...#this-viral-math-question-has-two-solutions-1
In particular, look at the 6/2(1+2) example. People really get confused by it with some thinking its
##\frac {6} {2} (1+2) = 9## versus some thinking its ## \frac {6} { 2 * (1+2)} = 1##

Do you see the confusion and why the first one is how we interpret the expression with modern PEMDAS conventions?

What is a combination?

A combination is a selection of items from a larger set, where the order of the items does not matter. For example, choosing 3 toppings from a list of 5 toppings for a pizza is a combination.

How do I calculate the number of combinations?

The formula for calculating the number of combinations is nCr = n! / r!(n-r)!, where n is the total number of items and r is the number of items being chosen. This formula is also known as the combination formula.

What is the difference between combinations and permutations?

The main difference between combinations and permutations is that in combinations, the order of the items does not matter, whereas in permutations, the order does matter. In other words, combinations are about choosing, while permutations are about arranging.

What are some real-life applications of combinations?

Combinations are used in various fields such as mathematics, statistics, and computer science. Some real-life applications include creating passwords, lottery numbers, and sports betting.

How can I improve my problem-solving skills for combination questions?

To improve your problem-solving skills for combination questions, it is important to practice and familiarize yourself with the formulas and concepts. You can also try breaking down the problem into smaller, simpler parts and using visual aids such as diagrams or charts to help you understand the problem better.

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