# Permutation and combination

by look416
Tags: combination, permutation
 P: 87 1. The problem statement, all variables and given/known data a computer terminal displaying text can generate 16 different colours numbered 1 to 16. any one of colours 1 to 8 may be used as the "background colour" on the screen, and any one of colours 1 to 16 may be used as the " text colours"; however, selecting the same colour for background and text renders the text invisible and so this combination is not used. find the number of different usable combinations of background colour and text colour. 2. Relevant equations nCr nPr 3. The attempt at a solution i have using 16 P 8 x 16 P 16 where 16P8 refers as the possible combinations of background colours and 16P16 is the possible combinations of text colours by multiplying both probability, and find the answer...
 P: 392 Fundamental Principle of Counting: If Step 1 can be done m ways, and after it is done, Step 2 can be done n ways, then both of these steps can be done in this order in m times n ways. Step 1 is pick one background colour. (How many background colours are there?) Step 2 is pick one text colour.
P: 87
 Quote by Billy Bob Fundamental Principle of Counting: If Step 1 can be done m ways, and after it is done, Step 2 can be done n ways, then both of these steps can be done in this order in m times n ways. Step 1 is pick one background colour. (How many background colours are there?) Step 2 is pick one text colour.
As what you have said,
8 background colours there , therefore i use 8C1
16 text colours there, therefore i use 16C1
result is 8C1 x 16C1 = 128