Question

From a pack of n cards numbered 1 to n 5 cards are drawn at random what is the probability that these cards wil be drawn in ascending order

Answer 1

Original answer is 1/30.

I don´t get it and would appreciat th help.

My approach was: Denominator: (6*5*4*/3!) = 20

Numerator: I just know, that there are four groups of ascending numbers (1,2,3)(2,3,4)(3,4,5)(4,5,6).

Answer 2

Answer:

$\frac{1}{(n-1)!}$ is the probability of cards drawn in ascending order.

Step-by-step explanation:

Step 1 of 3

Sample space = {$1,\ 2,\ 3,\ .\ .\ .\ , n$}

The total number of cards = $n$

Given that $5$ cards are drawn at random. Then,

The total number of ways of selecting $5$ cards = $nP_5$

                                                                              = $\frac{n!}{5!}$

Step 2 of 3

The number of ways of selecting $5$ cards out of $n$ in ascending order,

= $n_C_5$

= $\frac{n!}{5!(n-1)!}$ ways

Step 3 of 3

Probability that cards drawn are in ascending order,

= (No. of ways of selecting $5$ cards in ascending order)/(Total no. of ways of selecting $5$ cards)

= $\frac{\frac{n!}{5!(n-1)!}}{\frac{n!}{5!} }$

= $\frac{1}{(n-1)!}$

Therefore, probability of cards in ascending order is $\frac{1}{(n-1)!}$.

#SPJ2