SOLUTION: Ten pencils and eight pens are in a box. Eleven writing utensils are to be selected at random, without replacement, from the box. If the pens and pencils are equally likely to be s

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Ten pencils and eight pens are in a box. Eleven writing utensils are to be selected at random, without replacement, from the box. If the pens and pencils are equally likely to be s      Log On


   

Question 1204884: Ten pencils and eight pens are in a box. Eleven writing utensils are to be selected at random, without replacement, from the box. If the pens and pencils are equally likely to be selected, use combinations to determine the probability that seven pencils and four pens are selected.
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


The denominator of the probability fraction is the number of ways you can choose 11 of the 18 pens and pencils -- "18 choose 11":

C%2818%2C11%29=31824

The numerator of the probability fraction is the number of ways you can choose 7 of the 10 pencils and 4 of the 8 pens:

%28C%2810%2C7%29%29%2A%28C%288%2C4%29%29=120%2A70=8400

ANSWER: 8400%2F31284

Simplify the fraction and/or convert to a decimal or a percentage if needed.