There are seven competitors in the jured art showcase in how many ways may the judges choose a winner
and a fost runner-up)

The number of ways in which the judge can choose the  winner  and a first runner up = 42

Step-by-step explanation:

Step 1 :

Number of competitors in the art show case = 7

We need to find the number of ways the judges can choose the winner and the first runner up.

Step 2 :

The number of ways using which the judge can choose the winner = 7

(Since there are 7 competitors)

The number of ways using which the judge can choose the first runner up = 6

(Since the winner is already chosen, the remaining number of competitors will be 7 - 1 =6)

Hence the number of ways in which the judge can choose the  winner  and a first runner up = 7 × 6 = 42

Step 3 :

Answer :

The number of ways in which the judge can choose the  winner  and a first runner up = 42