+0

# Finite help

0
68
2

Assume that the student has a cup with 12 writing implements: 6 pencils, 4 ball point pens, and 2 felt-tip pens. In how many ways can the selection be made if no more than one ball point pen is selected if they must choose 4 implements?

Guest Sep 5, 2017
Sort:

#1
+76145
0

CPhill  Sep 5, 2017
edited by CPhill  Sep 5, 2017
edited by CPhill  Sep 6, 2017
#2
+18564
0

Assume that the student has a cup with 12 writing implements: 6 pencils, 4 ball point pens, and 2 felt-tip pens. In how many ways can the selection be made if no more than one ball point pen is selected if they must choose 4 implements?

$$\begin{array}{|rcll|} \hline && \binom{4}{1}\binom{8}{3} + \binom{4}{0}\binom{8}{4} \\ &=& 4\binom{8}{3} + 1\binom{8}{4} \\ &=& 4\cdot \frac{8}{3}\cdot \frac{7}{2}\cdot \frac{6}{1} + \frac{8}{4}\cdot \frac{7}{3}\cdot \frac{6}{2}\cdot \frac{5}{1} \\ &=& 4\cdot 8 \cdot 7 + 7 \cdot 2 \cdot 5 \\ &=& 224 + 70 \\ &=& 294 \\ \hline \end{array}$$

heureka  Sep 6, 2017

### 12 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details