The Number of 4-digit numbers containing at least one 8? Show Steps...?

Answer 1

number of 4 digit numbers = 9*10*10*10 = 9,000

Why only 9 in the thousands place? it cant be zero (four digit number), all other places may take the value 0.

number of 4 digit numbers without the digit 8
= 8 * 9 * 9 * 9 = 5,832

so number of 4 digit numers with at least one 8? The difference!

9,000 - 5,832 = 3,168

Answer 2

i'm going to agree with ten bong

your first 4 digit number is 1000
last one is 9999
thats 9000 possible numbers


So yeah.
for the 1000's place....there are only 8 possible numbers that one can use so there is no "8". 0 and 8 are the 2 numbers we can't use.
100's place. 9 possible numbers
10's place... 9
1's place 9
8*9*9*9 = 5832
9000-5832= 3168

Other way to do it
start with 1000
1008
1018
1028
1038
1048
1058
1068
1078
skip 1080's..we know there are 10 numbers here
1098.
So between 1000 and 1100 there are 19 numbers

we know there will be 19 for
1100-1200
1200-1300 ..etc
skip 1800-1900.
so we got 8
for 1800-1900...there will be 100
so 19*8+100 = 271
271 numbers with "8" between 1000-2000
same thing between 2000-3000....3000-4000..etc
skip 8000
there are 1000 numbers betrween 8000-9000 with "8"
so
271*8 +1000 =3168

Answer 3

case1: only 1 "8"
no. of digits=1*9*9*9*4!=17496

case2: 2"8"
no. of digits= 1*1*9*9*4!=1944

case3: 3"8"
no. of digits=1*1*1*9*4!=216

case4: 4"8"
no. of digits=1

Total=17496+1944+216+1
=19657

We multiply by 9 because the other digits can be 012345679, so there are 9 possibilities. Factorial to shuffle the digits around.

Answer 4

All possibilities
Possibilities for 1000s place --- 1,2,3,4..7,8,9 = 9
Possibilities for 100s place = 0,1,2,3,...7,8,9 = 10
Possibilities for 10s place = 0,1,2,3,...7,8,9 = 10
Possibilities for units place = 0,1,2,3,...7,8,9 = 10

Numbers containing no 8s
Possibilities for 1000s place --- 1,2,3,4..7,9 = 8
Possibilities for 100s place = 0,1,2,3,...7,9 = 9
Possibilities for 10s place = 0,1,2,3,...7,9 = 9
Possibilities for units place = 0,1,2,3,...7,9 = 9

Total number of 4-digit numbers = 9 * 10 * 10 * 10 = 9000
Number of 4 digit numbers with no 8s = 8 * 9 * 9 * 9 = 5832

Number of 4 digit numbers with at least one 8
= 9000 - 5832
= 3168