By using 0,1,2,3,4,5,6, how many 5 digit numbers are greater than 24000 but less than 54000 can be made ?
Answers
hope it was helpful
Step-by-step explanation:
By 0, 1, 2, 3, 4, 5, 6, how many numbers of 5 digits are greater than 24,000 can be made?
Assuming repetition is not allowed, we have:
4 choices for the first digit (one of 3, 4, 5, 6) for 5-digit numbers greater than 30,000.
6 choices for the second digit (one of 0, 1, 2 and one of ( 3, 4, 5, 6 minus the 1st digit),
5 choices for the third digit, (any one of the remaining 5 digits)
4 choices for the fourth digit, (any one of the remaining 4 digits)
3 choices for the fifth digit. (any one of the remaining 3 digits)
Therefore,
4 * 6 * 5 * 4 * 3 = 1,440 5-digit numbers formed greater than 30,000 and therefore greater than 24,000.
For 5-digit numbers starting with 2 and greater than 24,000, w
with repetation
1st place except 0 and 1 - 5 numbers
2nd place all except 0 1 2 and 3 -3 numbers
3rd - all 7
4th -all 7
5th all 7
ans=7*7*7*5*3–1=5145–1=5144 {24000 is excluded so (5145–1)}
without repetation
5*3*5*4*3=900