Question

how many integers can be formed using one or more of the digits 2,5,6,7, and 8 if no digit is repeated in a number?

Answer 1

infinite

Answer 2

fail^

Answer 3

for one digit

there are 5 different numbers

Answer 4

for 2digits there are ( 5 x 4 ) = 20 different numbers

Answer 5

for 3 digits there are ( 5 x 4 x 3 ) = 60 different numbers

Answer 6

for 4 digits there are 5 x 4 x 3 x 2 = 120 different numbers

Answer 7

for 5 digits there are 5 x 4 x 3 x 2 x 1 = 120 different numbers

Answer 8

total number of different numbers = 5 + 20 + 60 + 120 + 120 = 325

Answer 9

thank you so much for your help! I checked the packet answers and the answer is 195....? if it helps this is our probability unit

Answer 10

oh i see! i left out a very important word in the problem... it says *even positive* integers!

Answer 11

well

thats means for one digit we have 3 different numbers

Answer 12

for two digits we have (3 x 4) = 12 different numbers

for three digits we have ( 3 x 4 x 3 ) = 36

for four digits we have ( 3 x 4 x 3 x 2 ) = 72

for all five digits we have (3 x 4 x 3 x 2 x 1 ) = 72

Answer 13

add them and you get the 195

Answer 14

basically , you need to deal with the restriction first

Answer 15

thank you! how did you know to multiply it by 4 and 3 though?

Answer 16

for it too be even it must end in either 2, 6 or 8 ( three different ways )

Answer 17

so , take the 2digit case, first of all we must pick the last digit such that the number will be even ( we can do this in 3 ways ) , then once we have selected the last digit there are 4 digits remaining from which we can pick the second digit

Answer 18

similarly with the other cases

Answer 19

e.g. four digit case , first we pick the last digit ( which can be done in 3 ways )

then we have 4 digits remaining with which to choose the remaining 3 digits

Answer 20

oh! thank you soo much! I really appreciate it!