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[tex]P_{r}[/tex]=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[tex]P_{3}[/tex]
=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 https://brainly.com/question/1216161
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