# Combination help

• Nov 3rd 2008, 11:56 PM
AltQQ
Combination help
Bill is making a sandwich. he may choose a combination of the following: lettuce, tomato, carrot, cheese, cucumber, beetroot, onion and ham. Find the probability that the sandwich contains ham.
• Nov 4th 2008, 02:06 AM
mr fantastic
Quote:

Originally Posted by AltQQ
Bill is making a sandwich. he may choose a combination of the following: lettuce, tomato, carrot, cheese, cucumber, beetroot, onion and ham. Find the probability that the sandwich contains ham.

Is Bill allowed to choose either 1, 2, 3, ...... up to all 8 of the sandwich fillings?
• Nov 4th 2008, 08:35 AM
pankaj
Number of all possible combinations $=2^8-1=255$

If ham has to be included,this can be done in 1 way and the others can be chosen in $2^7=128$ ways.

Required probability= $\frac{128}{255}$