There are 720 ways through which 3 numbers can be selected from 10 numbers to open a keypad lock.
Given that there are 10 numbers are 3 numbers are required to open a keypad lock.
Permutations are the number of ways in which objects can be selected without replacements to form subsets.
It is expressed as n
=n!/(n-r)!.
Factorial of a number is the product of consecutive numbers less than the number.
Total numbers available=10
Numbers to be selected=3
Number of ways can be found by using permutations.
Number of ways =10
=10!/(10-3)!
=10!/7!
=10*9*8*7!/7!
=10*9*8
=720 ways.
Hence there are 720 ways through which 3 numbers can be selected from 10 numbers.
Learn more about permutations at brainly.com/question/1216161
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Answer:
20ft
Step-by-step explanation:
We have two unknowns, the length and the width of the floor. Let us represent this by l and w respectively.
Firstly, we are told that the length of the floor is twice its width. This mathematically means that l = 2w
The width of the rectangular carpet is 2ft less than the width of the floor but the floor length is equal. This means that the width of the floor is (w - 2)ft
Now we are told that the area of the rectangular carpet is 160 sq.ft
This means the length of the carpet multiplied by the width is 160
Mathematically:
l * (w-2) = 160
We know that l = 2w, if we substitute this:
2w(w - 2) = 160
w(w -2) = 80
w^2 -2w = 80
w^2 - 2w - 80 = 0
w^2 -10w + 8w -80 = 0
w(w -10) + 8(w - 10) = 0
(w + 8)(w -10) = 0
w = -8 or 10
Since distance cannot be negative, we ignore the -8 and use the 10 only
Hence the width is 10ft
The length is 2 times the width. The length is thus 2 * 10ft = 20ft
1. 5-25=3x-4 => -20=3x-4 => -16=3x => x= -16/3
2. 1-2x=3-2x-2 => 1=3-2 => 1=1 => x=R
