The number of ways to choose 2 pens from 4 pens can be calculated using the combination formula ( \binom{n}{r} ), where ( n ) is the total number of items and ( r ) is the number of items to choose. Here, ( n = 4 ) and ( r = 2 ). Thus, the calculation is ( \binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6 ). Therefore, there are 6 ways to choose 2 pens from 4.
Let the cost of each pen be ( x ) cents. Since you buy ( x ) pens, the total cost can be expressed as ( x \times x = x^2 ) cents. Given that the total cost is 1.44 dollars, which is 144 cents, we have the equation ( x^2 = 144 ). Solving for ( x ), we find ( x = 12 ). Therefore, you bought 12 pens.
If there are ( p ) pens in a pack and 2 of them don't work, the expression for the number of working pens in the pack is ( p - 2 ). This represents the total number of pens minus the non-functioning ones.
Infinitely many ways, since if you have found one way then take one of the fractions and replace it by an equivalent fraction. Repeat for ever.
Three ways. 3 + 37 11 + 29 17 + 23
First, I would like to say that the whole question is not here. The question states: upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27 contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12 contained both a black pen and a pencil, 18 contained both a blue pen and a pencil and 10 contained all three items. How many backpacks contained none of the three writing instruments? OK I will explain this the best I can! Starting out, their are 10 backpacks that contain all the items. 12 contained both a black and blue pen. You would subtract 10 from 12; therefore there are 2 backpacks that contain only black and blue pens. 18 contain both a blue pen and a pencil. subtract 10 from 18 and you get 8. 15 contained both a black pen and a blue pen. You would subtract 10 from 15 and you get 5. There are 23 with black pens. So you would do 23 - (5+10+2)= 6. There are 6 backpacks that contain only black pens. There are 27 that contain blue pens. So you would do 27 - (5+10+8) = 4. There are 4 backpacks that contain only blue pens. There are 21 backpacks that contain a pencil. You would do 21 - (2+10+8) = 1. All together, there a 6 that contain only black pens, 5 that contain only black and blue pens, 4 that contain only blue pens, 10 that contain all three items, 2 that contain only black pens and pencils, 8 that contains only blue pens and pencils, and 1 that contains only 1 pencil. So you would add 6+5+4+10+8+2+1= 36. There are 38 backpacks, so you would subtract 36 from 38. There are 2 backpacks that contain none of the three writing instruments. Ashfords quiz says this is right.
24 ways. :)
10
20C2 = 190
The answer is 6C4 = 6*5/(2*1) = 15
36 x 35/2 ie 630
309*308/2 = 47586
1.204*1024 pens * (1 mole pens/6.022*1023 pens) = 1.9993 molesTherefore, 1.204*1024 pens is about 2 moles of pens.
20, without replacing the first book chosen. 25 with replacing it.
There are 26 red cards and 26 black cards. 3 red cards can be chosen in 26C3 ways 2 black cards can be chosen in 26C2 ways The required answer is 26C3 X 26C2 ways. Answer: 1067742 S Suneja
The answer is 118
If there are ( p ) pens in a pack and 2 of them don't work, the expression for the number of working pens in the pack is ( p - 2 ). This represents the total number of pens minus the non-functioning ones.
5 pens for 38.99 is the better deal.