Answer – Permutation refers to the arrangement of elements in a specific order while choosing a subset from a larger set, whereas combination refers to selecting elements from a set without considering their order.

Explanation:

Permutation and combination are two popular but different concepts in combinatorial mathematics. They are used to count the number of ways to select or arrange elements from a set without repetition. The main difference lies in whether the order of the selected elements matters or not.

Here is an example: 

For a bag with three colored balls [red (R), blue (B), and green (G)], if one wants to select only two balls at a time, the permutations for this selection would be:

• Red ball, blue ball (RB)
• Red ball, green ball (RG)
• Blue ball, red ball (BR)
• Blue ball, green ball (BG)
• Green ball, red ball (GR)
• Green ball, blue ball (GB)

The colors are in a specific order of arrangement (red with blue and green, then blue with red and green, and so on). After exhausting an order of one color, the selection is moved to another one in a methodical fashion.

If the same bag of balls is subjected to a combination of picking two balls at a time, here are the possible combinations:

• Red ball, blue ball (RB)
• Red ball, green ball (RG)
• Blue ball, green ball (BG)

In this case, the pairings of balls are considered without caring about the order in which they were selected. Therefore, RB and BR are considered as the same combination, much like RG and GR, and BG and GB.

Some real-life examples of permutation include seating arrangements for people at a dinner party or drawing out numbers for a lottery, where order decides the outcome. Forming a sports team or prepping toppings for a sundae ice cream is purely a matter of combination; the order is not significant in these cases.

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