Final answer:
To compute the number of ways to pick a set of three blocks such that at least one block is odd, subtract the combinations of three even or indistinguishable blocks from the total combinations of any three blocks.
Step-by-step explanation:
To find the number of ways to pick a set of three blocks from eight, where each set contains at least one odd block, we first identify the odd numbered blocks. There are three odd blocks, labeled 1, 3, and 5. Picking at least one odd block means we can have all three as odd, two as odd and one as even or indistinguishable, or one odd and two even or indistinguishable.
The total number of ways to pick three blocks without restriction is a combination of eight items taken three at a time. The number of ways to pick three blocks without any odd blocks is a combination of the five items that are even or indistinguishable taken three at a time.
The total number of combinations with at least one odd block is then calculated by subtracting the number of all even/indistinguishable combinations from the total number of combinations. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of items and k is the number of items to choose.
To answer this, we calculate:
- Total combinations of any three blocks from eight: C(8, 3)
- Combinations of three blocks from the five that are even or indistinguishable: C(5, 3)
- Finally, subtract the second from the first to find the answer.
The calculation will provide the number of combinations where at least one block is odd.