A box contains coupons labelled 1,2, ldots, 1 | vedclass

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Question

(c)

We have,$100$ coupons labelled $1$ , $2,3, \ldots 100$

Five coupons are random selected and arranged.

$	herefore$ Total numbers of outco

Vedclass · Accepted Answer

$1 / 20$

Vedclass · Answer

(c) We have,$100$ coupons labelled $1$ , $2,3, \ldots 100$ Five coupons are random selected and arranged. $ herefore$ Total numbers of outcomes $={ }^{110} C_5 imes 5$ ! Five coupons $x_1, x_2, x_3, x_4, x_5$ are arranged such that $x_1 > x_2 > x_3$ and $x_3 < x_4 < x_5$ Favourable outcomes $={ }^{100} C_5 imes \frac{4 !}{2 ! 2 !}$ $ herefore ext { Required probability } =\frac{{ }^{100} C_5 imes \frac{4 !}{2 ! 2 !}}{{ }^{100} C_5 imes 5 !}$ $=\frac{1}{20}$

A box contains coupons labelled $1,2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x _3 < x _4 < x _5 ?$

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