How many numbers of 4 digits each greater than 5000 can be formed from the digits 1,2,3,4,5,6,7?..help plzz..

Question

agent0smith · Answer

Three choices for the first digit (5, 6 or 7 are the only ones to make 4 digit numbers > 5000) then 7 choices for the remaining digits, so it should be...

3*7*7*7 = ?

anonymous · Answer

1029??

agent0smith · Answer

@Luis_Rivera what...? Not sure what you meant, but 0 isn't an choice, so all 5xxx are greater than 5000.

agent0smith · Answer

Smallest number we can make with 1,2,3,4,5,6,7 which is greater than 5000 is 5111, so there's 3 options, 5 6 and 7 for the first digit.

agent0smith · Answer

uh, why not...?

agent0smith · Answer

@Luis_Rivera "How many numbers of 4 digits each greater than 5000 can be formed from the digits 1,2,3,4,5,6,7?"

Here, 5xxx is greater than 5000... i'm not following you...

anonymous · Answer

so what are the answer?

anonymous · Answer

is*

agent0smith · Answer

$$ \large 3*7^3$$

anonymous · Answer

if without repeating numbers??

agent0smith · Answer

W/o repeating it'll be...

3*6*5*4

kropot72 · Answer

Taking 5 as the first digit there are 6P3 permutations of the remaining 6 digits.
Taking 6 as the first digit there are 6P3 permutations of the remaining 6 digits.
Taking 7 as the first digit there are 6P3 permutations of the remaining 6 digits.
Total number of permutations are
$$3\times 6P3=3\times \frac{6!}{3!}=360$$

agent0smith · Answer

^correct, for no repetition.

anonymous · Answer

thanks

anonymous · Answer

without repeating=360..repeating - 28800???....3x6P3x5p2x4p1?

agent0smith · Answer

^ no, with repeating it's 3*7*7*7 = 3*7^3 = 1029