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To solve the problem of finding the number of ways to select 5 cards from a standard deck with at least one face card and at least one non-face card, follow these steps:

Step 1: Key Counts

• Total cards: 52
• Face cards (Jack/Queen/King): 12 (3 per suit × 4 suits)
• Non-face cards: 52 - 12 = 40

Step 2: Total 5-card hands

[ \binom{52}{5} = 2598960 ]

Step 3: Hands with no face cards

[ \binom{40}{5} = 658008 ]

Step 4: Hands with no non-face cards (all face cards)

[ \binom{12}{5} = 792 ]

Step 5: Desired hands

Subtract the invalid cases from the total:
[ 2598960 - 658008 - 792 = 1940160 ]

Answer: (\boxed{1940160})

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