Question:
The number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination is:
The number of 5-card combinations out of a deck of 52 cards if there is exactly one ace in each combination is:
Show Hint
For combinations with a specific element, first choose that element and then choose the remaining from the rest.
Updated On: Jul 18, 2026
- 823764
- 363428
- 778320
- 542380
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Choose 1 ace.
There are 4 aces in the deck, choose 1: \[ \binom{4}{1} = 4 \]
Step 2: Choose remaining 4 cards.
There are 48 non-ace cards remaining, choose 4: \[ \binom{48}{4} = 194580 \]
Step 3: Total combinations.
Multiply choices of ace and non-aces: \[ 4 \cdot 194580 = 778320 \]
Step 4: Final answer.
\[ \boxed{778320} \]
There are 4 aces in the deck, choose 1: \[ \binom{4}{1} = 4 \]
Step 2: Choose remaining 4 cards.
There are 48 non-ace cards remaining, choose 4: \[ \binom{48}{4} = 194580 \]
Step 3: Total combinations.
Multiply choices of ace and non-aces: \[ 4 \cdot 194580 = 778320 \]
Step 4: Final answer.
\[ \boxed{778320} \]
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