HELP WILL MARK BRAINLIEST
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Answer:
Step-by-step explanation:
Given : universal set in this diagram is the set of integers from 1 to 15.
Solution :
The intersection of odd integer,multiples of 3 and Factors of 15 are 3,15
The intersection of odd integer and Factors of 15 are 1,5
The intersection of odd integer,multiples of 3 is 9
The remaining multiples of 3 are 6,12
The remaining odd integers are 7,11,13
Now the remaining integers are 2,4,8,10,14 and these integers must be placed in the boxes outside the circles Since they does not belong any intersection or odd integer or factor of 15 .
Refer the attached figure for the answer.
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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