I've been recently studying probability and I'm pretty much stuck with analyzing the difference between finding sample space of rolling a pair of dice simultaneously and drawing two cards simultaneously from a pack of 10 cards each card numbered 1 to 10. In the first case, the sample space is 36 that is we consider all the possible pairs (for example the pairs (1, 2) and (2, 1)) are treated separately. But in the second case the sample space is 10C2 (that is here the pairs are considered the same). My doubt is that in the first case since the dice are rolled simultaneously why can't we consider the pairs as the same which when considered the sample space for first case becomes 21 but not 36?
2026-03-10 08:42:02.1773132122
Difference between finding the sample space of rolling a pair of dice simultaneously and two cards drawn at random from a pack simultaneously?
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