Answer:
133,784,560
Step-by-step explanation:
using the combinations formula: n!/(n-r!)r!, the equation would be 52!/52-7! x 7! which is simplified to 52!/45!7! which is equal to 133,784,560
The number of ways of selecting 7-cards with 2 hearts, 2 diamonds, 2 clubs, and 1 spade is 1,169,176.
A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades.
The number of ways of selecting 7-cards with 2 hearts, 2 diamonds, 2 clubs, and 1 spade will be
[tex]\rm Number \ of \ the \ ways = ^{13}C_2 \times ^{13}C_2\times ^{13}C_2\times ^{13}C_1[/tex]
[tex]\rm Number\ of \ the \ ways=78\times 78\times 78\times 13[/tex]
[tex]\rm Number \ of \ the \ ways= 6,169,176[/tex]
The number of ways is 6,169,176.
More about the permutation and the combination link is given below.
brainly.com/question/11732255
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