How many positive integers n can we form using the digits 3, 4, 4, 5, 5, 6, 7 if we want n to exceed 5,000,000?
Answers
Answer:
=180. The total of numbers n > 5, 000, 000 is equal to the number of arrangements of 3, 3, 4, 5, 6, 7 of size 6; thus, 6!
Explanation:
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The number positive numbers can be formed = 360
Given:
The set digits 3, 4, 4, 5, 5, 6, 7
To find:
How many positive integers 'n' can we form using the digits if we want n to exceed 5,000,000?
Solution:
Digits are 3, 4, 4, 5, 5, 6, 7
Number of digits = 7
To make a positive integer that exceeds 5,000,000 we need to keep 5, 5, 6, and 7 in 1st position of the resultant number
∴ Number of ways that 1st position can be taken = 3 [ i.e 5, 5, 6, and 7 ]
After taking 1st number remaining numbers = 6
∴ Number of ways that 2nd number can be taken = 6
After taking 2st number remaining numbers = 5
∴ Number of ways that 3rd number can be taken = 5
After taking 3st number remaining numbers = 4
∴ Number of ways that the 4th number can be taken = 4
After taking 4th number remaining numbers = 3
∴ Number of ways that the 5th number can be taken = 3
After taking 5th number remaining numbers = 2
∴ Number of ways that the 6th number can be taken = 2
After taking 6th number remaining numbers = 1
∴ Number of ways that the 7th number can be taken = 1
From the above explanation
Total number of ways = (3× 6 × 5 × 4 × 3 × 2 × 1)/2!
[ since there are two 4 s ]
= 720/2 = 360
Therefore,
The number positive numbers can be formed = 360
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