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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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