a student has ten posters to pin up on the wall of her room, but there is space for only seven. in how many ways can she choose the posters to be pinned on the wall?

Writeacher, nice answer showing how mathematicians often assume what to them appears obvious, resulting in poor wording of the question.

number of ways to choose 7 from 10
= C(10,7) = 10!/(3!7!) = 120

10C7

Well, the student has quite the poster predicament, doesn't she? It seems she has ten posters but only room for seven. So, let's solve this puzzle!

To figure out the number of ways she can choose the posters, we can use a combination formula. The formula goes like this:

C(n, r) = n! / (r!(n-r)!)

In this case, n represents the total number of posters (which is 10) and r represents the number of available spaces on the wall (which is 7).

So, applying the formula, we have:

C(10, 7) = 10! / (7!(10-7)!)

Now, let's do some clown-calculations!

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

10-7 = 3

(10-7)! = 3! = 3 x 2 x 1 = 6

So now, plugging these values into our equation, we get:

C(10, 7) = 3,628,800 / (5,040 x 6)

And when we simplify this, we find:

C(10, 7) = 120

Therefore, she can choose the posters in 120 different ways! Quite the variety, huh?

To determine the number of ways the student can choose the posters to be pinned on the wall, we can use a combination formula.

The combination formula is given by:

C(n, r) = n! / (r! * (n-r)!)

where:
- C(n, r) represents the number of combinations of n items taken r at a time
- n! represents the factorial of n (n * (n-1) * (n-2) * ... * 1)

In this case, the student has 10 posters and there is space for only 7. Therefore, we need to find C(10, 7).

Plugging in the values into the formula, we get:

C(10, 7) = 10! / (7! * (10-7)!)

Simplifying further:

C(10, 7) = 10! / (7! * 3!)
= (10 * 9 * 8 * 7!)/(7! * 3!)
= (10 * 9 * 8)/(3 * 2 * 1)
= 10 * 3 * 4
= 120

Therefore, there are 120 ways the student can choose the posters to be pinned on the wall.

Umpteen ways by making a collage!!

http://image.shutterstock.com/z/stock-photo-travel-in-italy-vintage-collage-113500528.jpg