Question

A four digit number (with no repetitions) is to be formed from the set of numbers {0,1,2,3,4,5,6,7}. Find the probability that the number
a) is even
b) is odd
c) is less than 4000
d) is less than 4000, given that it is greater than 3000

Answer 1

it should be somewhat obvious that it has a 50% chance of being either even or odd
if it ends in even number, then its even
if ends with odd, then its odd
there are equal amount of odd/even numbers in set

Answer 2

could u first find how many 4 digits number could be made ?
no @dumbcow .

Answer 3

there are 8*7*6*5 possible numbers .... 1680

for each "thousand", there are 7*6*5 possible numbers ... 210
meaning 210 possible numbers between 0 and 999
210 possible numbers between 1000 and 1999
and so on ...

Answer 4

part d is simplest:
numbers greater than 3000 can start with 3, 4, 5, 6 or 7
numbers from the above sample space less than 4000 have to start with 3
reqd. probability
= 1/5
= .2

Answer 5

to form a 4 digit number,u cannot use those first 210 numbers in 0 to 999
so the total numbers that can be formed are 7*7*6*5=1470 or 1680-210=1470

Answer 6

for part c.)
the 1st digit can only be 1,2,3 for number to be <4000
the 2nd digit could be any of the remaining 7,3rd digit any of the remaining 6,4th digit any of the remaining 5
so the probability=3*7*6*5/7*7*6*5=3/7
got this?