15 girls are seated at a round table. The num | vedclass

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(D) The total number of ways to select $3$ girls from $15$ girls seated around a round table is given by the combination formula ${}^{15}C_3$.First,we

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$440$

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(D) The total number of ways to select $3$ girls from $15$ girls seated around a round table is given by the combination formula ${}^{15}C_3$.First,we calculate the total number of ways to select $3$ girls: ${}^{15}C_3 = \frac{15 	imes 14 	imes 13}{3 	imes 2 	imes 1} = 5 	imes 7 	imes 13 = 455$.Next,we find the number of ways to select $3$ girls such that they are all seated together. In a circular arrangement of $15$ girls,there are $15$ possible sets of $3$ consecutive girls.So,the number of ways to select $3$ girls sitting together is $15$.Therefore,the required number of ways where all three are not seated together is $455 - 15 = 440$.

$15$ girls are seated at a round table. The number of ways of selecting three girls such that all the three are not seated together is

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