Counting - Day 2
Solutions
OR = addition AND = multiplication
1) 4 choices to get from A to B AND then 3 choices to get from B to C
4 * 3 = 12 ways
2) Your path is either A-B-D OR A-C-D
A to B and then B to D OR A-C and C-D
2 * 2 + 2 * 1
4 + 2 = 6 ways
3) For a 4-digit number you have to pick a number for the 1st spot. 7 choices available.
AND then you pick a number for the 2nd spot. Since we use 1 of our numbers...6 choices remain.
AND then you pick a number for 3rd spot ... down to 5 numbers available.
AND then you pick for 4th spot....only 4 numbers available.
7 * 6 * 5 * 4 = 840
4) For a 4-digit number you have to pick a number for the 1st spot. 7 choices there.
AND then you pick a number for the 2nd spot. Since we can reuse numbers...7 choices again.
AND then you pick a number for 3rd spot AND then you pick for 4th spot.
7 * 7 * 7 * 7 = 2401
5) no repetition: last digit must be 2 OR 4 OR 6
1st digit can be one of the 6 remaining choices same logic same logic
2nd digit can be one of 5 choices left after that
3rd digit can be one of 4 remaining numbers
6 * 5 * 4 * 1 + 6 * 5 * 4 * 1 + 6 * 5 * 4 * 1
120 + 120 + 120 = 360 ways
repetition allowed: 7 * 7 * 7 * 3 (last choice is one of the 3 even numbers to make and even 4-digit number)
OR = addition AND = multiplication
1) 4 choices to get from A to B AND then 3 choices to get from B to C
4 * 3 = 12 ways
2) Your path is either A-B-D OR A-C-D
A to B and then B to D OR A-C and C-D
2 * 2 + 2 * 1
4 + 2 = 6 ways
3) For a 4-digit number you have to pick a number for the 1st spot. 7 choices available.
AND then you pick a number for the 2nd spot. Since we use 1 of our numbers...6 choices remain.
AND then you pick a number for 3rd spot ... down to 5 numbers available.
AND then you pick for 4th spot....only 4 numbers available.
7 * 6 * 5 * 4 = 840
4) For a 4-digit number you have to pick a number for the 1st spot. 7 choices there.
AND then you pick a number for the 2nd spot. Since we can reuse numbers...7 choices again.
AND then you pick a number for 3rd spot AND then you pick for 4th spot.
7 * 7 * 7 * 7 = 2401
5) no repetition: last digit must be 2 OR 4 OR 6
1st digit can be one of the 6 remaining choices same logic same logic
2nd digit can be one of 5 choices left after that
3rd digit can be one of 4 remaining numbers
6 * 5 * 4 * 1 + 6 * 5 * 4 * 1 + 6 * 5 * 4 * 1
120 + 120 + 120 = 360 ways
repetition allowed: 7 * 7 * 7 * 3 (last choice is one of the 3 even numbers to make and even 4-digit number)