A person has 8 friends, of whom 5 will be invited to a party.

A person has 8 friends, of whom 5 will be invited to a party.


J
Asked by 2 years ago
240 points

A person has 8 friends, of whom 5 will be invited to a party.
(a) How many choices are there if 2 of the friends are feuding and will not attend together?
(b) How many choices if 2 of the friends will only attend together?

A person
jeffp

1 Answer

Answered by 2 years ago
8.7k points

part (a) The total number of choices will be choosing 5 from the 8 order not mattering minus those groups who include the feuding friends,

$$\begin{pmatrix} 8 \\ 5 \end{pmatrix} - \begin{pmatrix} 2 \\ 2 \end{pmatrix} \begin{pmatrix} 6 \\ 3 \end{pmatrix} = 36$$

part (b) If the two friends are not included in the group than we can get $\begin{pmatrix} 6 \\ 5 \end{pmatrix}$ friends. If the two friends are included then we can get $\begin{pmatrix} 2 \\ 2 \end{pmatrix} \begin{pmatrix} 6 \\ 3 \end{pmatrix}$ friends. These are mutually exclusive events for a total of,

$$ \begin{pmatrix} 6 \\ 5 \end{pmatrix} + \begin{pmatrix} 2 \\ 2 \end{pmatrix} \begin{pmatrix} 6 \\ 3 \end{pmatrix} = 26$$

Your Answer

Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0$ or $$\beta^2-1=0$$

Use LaTeX to type formulas and markdown to format text. See example.

Sign up or Log in

  • Answer the question above my logging into the following networks
Sign in
Sign in
Sign in

Post as a guest

  • Your email will not be shared or posted anywhere on our site
  •  

Stats
Views: 53
Asked: 2 years ago

Related