1995 AMC 8 Problem 23

Attempt Problem 23 of the 1995 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1995 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

23.

How many four-digit whole numbers are there such that the leftmost digit is odd, the second digit is even, and all four digits are different?

11201120

14001400

18001800

20252025

25002500

Answer: B
Concepts:multiplication principle
Difficulty rating: 1220
Solution:

The first digit is odd: 55 choices. The second is even: 55 choices (none of which repeats the odd first digit).

The third digit is any of the 88 unused digits, and the fourth is any of the 77 remaining. In total, 5×5×8×7=1400.5 \times 5 \times 8 \times 7 = 1400.

Thus, the correct answer is B .

← Problem 22#22
Full Exam

Problem 23 in Other Years

1985 AMC 8 · 1986 AMC 8 · 1987 AMC 8 · 1988 AMC 8 · 1989 AMC 8 · 1990 AMC 8 · 1991 AMC 8 · 1992 AMC 8 · 1993 AMC 8 · 1994 AMC 8 · 1996 AMC 8 · 1997 AMC 8 · 1998 AMC 8 · 1999 AMC 8 · 2000 AMC 8 · 2001 AMC 8 · 2002 AMC 8 · 2003 AMC 8 · 2004 AMC 8 · 2005 AMC 8 · 2006 AMC 8 · 2007 AMC 8 · 2008 AMC 8 · 2009 AMC 8 · 2010 AMC 8 · 2011 AMC 8 · 2012 AMC 8 · 2013 AMC 8 · 2014 AMC 8 · 2015 AMC 8 · 2016 AMC 8 · 2017 AMC 8 · 2018 AMC 8 · 2019 AMC 8 · 2020 AMC 8 · 2022 AMC 8 · 2023 AMC 8 · 2024 AMC 8 · 2025 AMC 8 · 2026 AMC 8