Introduction to the product rule

[sapiental]

Homework Statement

a) How many bit strings are there of length 8?

b) How many bit strings are there of length 8 which begins with 2 1's?

Homework Equations

Product Rule

The Attempt at a Solution

a) Since a bit string is either 0 or 1 there are two possibilities for each one. By the rule of products 2^8 = 256 bit strings.

c) the first two choices are fixed so its 11(0/1)(0/1)(0/1)(0/1)(0/1)(0/1)

2^6 = 64 possible different bit strings.

when u allow the preceding 1 to change u basically double the 64 combinations and allowing the first one u quadruple it getting back to the original 256.


Could someone please confirm my result. Danke!

 

[jhicks]

In short: Yes.