Solution

Statement:

The Correct answer is Option 3: 68880

Detailed Explanation:

Option 1: 1722

• This option is incorrect as the calculation does not account for the total number of cards and the factorial arrangement properly.
• The number of ways to choose 3 cards without replacement is calculated using permutations since the order matters.
• The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of cards and r is the number of cards chosen.
• For this case, P(42, 3) should be computed, not 1722.

Option 2: 1752

• This option is also incorrect because similar to Option 1, the calculation does not follow the correct permutation formula.
• The value of 1752 does not match the correct permutation formula for selecting and arranging 3 cards from a pack of 42 cards.

Option 3: 68880

• This is the correct answer.
• To calculate the number of ways to choose and arrange 3 cards from a pack of 42 cards without replacement, we use the permutation formula: P(42, 3) = 42 × 41 × 40 = 68880.
• Here, the first card can be chosen in 42 ways, the second card in 41 ways, and the third card in 40 ways, resulting in a total of 68880 ways.

Option 4: 6880

• This option is incorrect because the value is significantly lower than the correct permutation result.
• The calculation appears to ignore the proper multiplication of possibilities for the arrangement of 3 cards.

Option 5:

• This option is left blank and does not represent a valid answer.
• It does not contribute to the solution, as the correct permutation result is already established.