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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:
A) y^3+27
Step-by-step explanation:
There are two ways of solving this problem:
1. Recognizing this as the factored form of the sum of perfect cubes
2. Distribute and add the like terms.
1. In order to distribute we must multiply y by y^2-3y+9, and then 3 by y^2-3y+9:
After we add the positive and negative 3y^2 and 9y, they will cancel out and be gone entirely:
2. You know how you can factor the difference of perfect squares?
As an example:
Well, not many people know this but you can actually factor both the sum and difference of perfect cubes:
Because we have these identities, we can easily establish here that we have the sum of perfect cubes, and that (y+3)(y^2-3y+9)= y^3+3^3 = y^3+27