Question

consider the word PEPPERCORN
a.how many different strings can be made from this word when all letters are used
b.how many different start and end with p
c.in how many strings are the 3 letters P consecutive

Answer 1

if the letters were all different it would be \(10!\) but since you cannot tell the 3 Ps apart, or the 2 Es or the 2 Rs it is
\[\frac{10!}{3!2!2!}\]

Answer 2

why divide and not subtract

Answer 3

good question

Answer 4

it is the counting principle
since you cannot tell the 3 Ps apart, for example, when you compute 10! you have over-counted by the number of ways you can permute the 3 P's
there are 3!=6 ways but that doen't mean you counted 6 extra ways, it means you over-counted by a factor of 6

Answer 5

Ahh thnx :D

Answer 6

can you please answer part B and C?