+0

# Probability

+1
142
1

Fiona writes a list containing all the four-digit numbers that can be written using only the digits 1, 2, and 3. What is the probability that a randomlychosen number in Fiona's list has a digit-sum that is at least 6?

For example, 1,322 is such a number scine 1+3+2+2=8 is at least 6.

Apr 16, 2022

#1
+9461
+1

It is quite complicated to consider those numbers which have a digit sum that is at least 6.

We can consider those numbers which have a digit sum less than 6 instead.

Numbers with digit sum 4: 1111

Numbers with digit sum 5: 2111, 1211, 1121, 1112

Therefore, there are only 5 numbers with a digit sum less than 6. All other numbers have a digit sum of at least 6.

Note that there are 3^4 = 81 numbers which can be written with only 1, 2, 3.

$$\text{Required number} = 3^4 - 5 = 76$$.

Apr 16, 2022

#1
+9461
+1

It is quite complicated to consider those numbers which have a digit sum that is at least 6.

We can consider those numbers which have a digit sum less than 6 instead.

Numbers with digit sum 4: 1111

Numbers with digit sum 5: 2111, 1211, 1121, 1112

Therefore, there are only 5 numbers with a digit sum less than 6. All other numbers have a digit sum of at least 6.

Note that there are 3^4 = 81 numbers which can be written with only 1, 2, 3.

$$\text{Required number} = 3^4 - 5 = 76$$.

MaxWong Apr 16, 2022