Please show us what you think the answers should be.
Given the digits 1,2,3,4 and5 find how many 4-digit numbers can be formed from them:
(a)if the number must be even,without any repeated digit
(b)if the number must be even
(c)if repetitions of a digit are allowed
i'm not sure in my answer. Please answer to me.
thank you.
1.how many natural numbers greater than or equal to 1000 and less than 5400 have the properties:
(a)no digit is repeated
[my ans.4(9*8*7)+(4*5*4)]
(b)the digits 2 and 7 do not occur
[my ans.3(7*7*7)+1+(3*4*4)
2.how many 6-digit numbers can be formed using {1,2,...,9}with no repetitions such that 1 and 2 do not occor in consecutive positions?
[my ans.(9*8*7*6*5*4)-(7*6*5*4*5)
3.how many positive integers less than 1,000,000 can be written using only the digits 7,8 and9? how many using only the digits 0,8 and9?
[my ans.3^1+3^2+...+3^6] and [my ans.3+2(3+3^2+...+3^5)]
Please check my answer. thank you.
Not even close.
Remember, I told you that for a) you had two cases:
First case the number ends in 2 so you have
Second case the number ends in 4 so you have
When you have two mutually exclusive cases for one event you add the two together giving 4! + 4!
Part b) is totally different. The numbers can be repeated. So for the first digit you have 5 choices, the second digit you have 5 choices, the third digit you have five choices, but for the fourth digit you only have 2 choices since the number must be even. How would you calculate that?