Discrete math Exercise How many different strings can be mad

Discrete math

Exercise: How many different strings can be made from the letters in the work PEPPER- CORN when all the letters are used? How may of the strings start and end with the letter P? How many strings have 3 consecutive Ps?

Solution

a)

since there are 3 P , 2 E , 2 R, 1 C , 1 O , 1 N

from theorem of combinotrics

total number of strings = 10! / 3! * 2! * 2! * 1! * 1! * 1!

= 151200

b)

since 1st and last letter fixed and 2 P have been exhausted

total number of strings

= 8!/2! * 2!

= 10080

c)

since there are eight ways 3 consecutive P s can be arranged

total number of strings = 8 * 7!/2! * 2!

= 10080