Washington may not have experience running an entire country, but he has leadership skills. He was the General of the Continental Army which he lead to the victory of the Revolutionary War. He practically started this country by leading it to victory.
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George Washington might've chosen the most experienced cabinet he could've selected. He chose Henry Knox for his Secretary of War, and Thomas Jefferson as his Secretary of State.
https://www.postermywall.com/index.php/poster/view/7cb0bd40eee6fab42673b3f58e55f187 (My Poster)