- #1

Alexsandro

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I tryed to do this question of many ways, but I couldn't reach the answer. Could someone help me ?

"Four shoes are taken at random from five differents pairs. What is the probability that there is at least one pair among them" ?

The answer to this question is below, but I don't know how I reach it:

1- {[itex]5 \choose 0[/itex].[itex]5 \choose 4[/itex] + [itex]5 \choose 1[/itex].[itex]4 \choose 3[/itex] + [itex]5 \choose 2[/itex].[itex]3 \choose 2[/itex] + [itex]5 \choose 3[/itex].[itex]2 \choose 1[/itex] + [itex]5 \choose 4[/itex].[itex]1 \choose 0[/itex]}/[itex]10 \choose 4[/itex].

"Four shoes are taken at random from five differents pairs. What is the probability that there is at least one pair among them" ?

The answer to this question is below, but I don't know how I reach it:

1- {[itex]5 \choose 0[/itex].[itex]5 \choose 4[/itex] + [itex]5 \choose 1[/itex].[itex]4 \choose 3[/itex] + [itex]5 \choose 2[/itex].[itex]3 \choose 2[/itex] + [itex]5 \choose 3[/itex].[itex]2 \choose 1[/itex] + [itex]5 \choose 4[/itex].[itex]1 \choose 0[/itex]}/[itex]10 \choose 4[/itex].

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