# Determine number of ways [duplicate]

How can we find with how many ways we can choose three subsets $A_1, A_2, A_3$ of $\{1,2,3, \dots, 9\}$ such that $A_1 \cap A_2 \cap A_3= \varnothing$ ? (their pairwise intersection can be non-empty)

Can you give me a hint?

## marked as duplicate by Robert Z, drhab, Asaf Karagila♦ set-theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 7 '18 at 7:05

• Are the sets distinguished? In other words, is the case $A_1 = A_2 = \emptyset, A_3 = \{1\}$ different from $A_1 = \{1\}, A_2 = A_3 = \emptyset$? – Brian Tung Jun 7 '18 at 6:53

• If the digit in the i-th index is 1, that means that the number i is a member of the subset $A_1$
• If the digit in the i-th index is 2, that means that the number i is a member of the subset $A_2$
• If the digit in the i-th index is 3, that means that the number i is a member of the subset $A_3$