Question

1. how many different sequences of 3 playing cards (from a single 52-card deck) exist?

22,100
24,804
132,600
140,608

Explanation:

Step1: Identify the problem type

This is a permutation problem since the order of the cards in the sequence matters. The formula for permutations of \( n \) objects taken \( r \) at a time is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 52 \) (total number of cards) and \( r = 3 \) (number of cards in each sequence).

Step2: Calculate the permutation

First, calculate \( n! = 52! \), \( (n - r)!=(52 - 3)!=49! \). Then \( P(52, 3)=\frac{52!}{49!}=52\times51\times50 \) (because \( \frac{52!}{49!}=52\times51\times50\times49! / 49!=52\times51\times50 \)).

Calculate \( 52\times51 = 2652 \), then \( 2652\times50 = 132600 \).

Answer:

132,600 (corresponding to the option with 132,600)