Need help please!!   1.How many ways can 6 runners be arranged on a running track that has 8 lanes (assume one runner per lane allowed only) 2.100g substance is left to evapourate. Each day it...

Need help please!!

 

1.How many ways can 6 runners be arranged on a running track that has 8 lanes (assume one runner per lane allowed only)

2.100g substance is left to evapourate. Each day it loses one-tenth of its weight at the beginning of the day. How many days elapse before it is less than half its original mass?

Asked on by hss12

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llltkl's profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted on

Assuming only one runner is allowed per lane, six runners can be arranged on a running track that has 8 lanes in `^8C_6` ways.

Therefore, the required number of ways = `^8C_6`

=`^8C_(8-6)`

=`^8C_2`

= `(8!)/((6!)*(2!))`

= `(8*7)/(2*1)`

= `56/2`

=`28`

Hence, six runners can be arranged on a running track that has 8 lanes in 28 ways.

As for the second question, post it in a separate question.

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