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3 + 5 = 4*b so 8 = 4*b Divide both sides by 4: 2 = b
There are 20 unique 5-card hands. Solution: First break apart the player card combinations. You can either use player card 1, player card 2, or both player cards 1 and 2 with the hand. Therefore, you are taking 5 cards, 3 at a time, when playing with both player cards, and 5 cards, 4 at a time, when playing with 1 player card. Mathematically, this can be expressed using the Binomial coefficient 2 x ( 5 choose 4 ) + ( 5 choose 3 ) = Number of possible 5-card hands. 5 choose 4 = 5 : This represents the combinations between 1 player card and 5 table cards, 4 at a time. (http://www.wolframalpha.com/input/?i=5+choose+4) 5 choose 3 = 10 : This represents the combinations between 2 player cards, and 5 table cards, 3 at a time. (http://www.wolframalpha.com/input/?i=5+choose+3) Thus, 2 x ( 5 ) + ( 10 ) = 20 . Further Information: All possible hand combinations are listed below. A and B are the two player cards. 0 through 5 are the five table cards. ----- A 1 2 3 4 A 2 3 4 5 A 3 4 5 1 A 4 5 1 2 A 5 1 2 3 B 1 2 3 4 B 2 3 4 5 B 3 4 5 1 B 4 5 1 2 B 5 1 2 3 A B 2 3 4 A B 3 4 5 A B 1 2 3 A B 4 5 1 A B 5 1 2 A B 4 5 2 A B 4 1 2 A B 5 1 3 A B 5 2 3 A B 1 3 5
a^7 - b^7 = (a - b)(a^6 + a^5.b + a^4.b^2 + a^3.b^3 + a^2.b^4 +a.b^5 + b^6)
(5*4)+(8*3) where *indicates to multiply, and the equations in parenthesis(5*4 and 8*3) are done before you add them, so 5*4=A, 8*3=B, then A+B. Not doing your homework for you. AND USE THE COMPUTER CALCULATOR!!
Multiplication is an abbreviation of addition: 4 x 5 is the same as: adding 4 together 5 times: 4 x 5 = 4 + 4 + 4 + 4 + 4 = 20; or adding 5 together 4 times: 4 x 5 = 5 + 5 + 5 + 5 = 20 When multiplying a negative number by a positive number, it can be thought of adding the negative number to itself the positive number of times. eg -4 x 5 = -4 + -4 + -4 + -4 + -4 = -20 eg -5 x 4 = -5 + -5 + -5 + -5 = -20 Adding a negative number is the same as subtracting the number (as a positive number): eg 7 + -3 = 7 - 3 = 4 eg -7 + -3 = -7 - 3 = -10