what is the probability of a 4 digit number formed using 2 , 3 , 7 , 8 is a perfect square number
Answers
Answer:
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Step-by-step explanation:
Total 4 digit numbers formed
4×4×3×2=96
Each of these 96 numbers are equally likely & mutually exclusive of each other.
Now, A number is divisible by 4, if last two digits of the number is divisible by 4
Hence we can have the following numbers in the last two digits
0
4:
first two places can be filled in 3×2=6 ways
1
2:
first two places can be filled in 2×2=4 ways
2
0:
6 ways
2
4:
4 ways
3
2:
4 ways
4
0:
6 ways
Total number of ways=6+4+6+4+4+6=30 ways
probability=
Totaloutcomes
favorableoutcomes
=
96
30
=
16
5
Given: A 4 digit number formed by using 2,3,7,8
To find: Probability of the number being a perfect square
Explanation: Total numbers that can be formed using 2,3,7,8= 4! (since 4 different digits are used)
= 24
For number to be a perfect square, the number should end with 1,4,9,6,5,0.
Taking examples: 22^2= 484( ends with 4)
46^2= 2116( ends with 6)
In the given question, none of the given numbers 2,3,7,8 matches with the numbers required to make it a perfect square. Therefore, no 4 digit number can be formed using 2,3,7,8 that is a perfect square.
Probability= Numbers that are perfect square/Total numbers
= 0/24= 0
Therefore, the probability of a 4 digit number formed by using 2,3,7 and 8 that is a perfect square is 0.