Aman is distributing his coin collection with 35 coins to his five grandchildren. how many ways are there to distribute the coins if:
a. the coins are all the same
b. the coins are all distinct
c. the coins are the same and each grandchild gets the same number of coins.
d. the coins are all distinct and each grandchild gets the same number of coins.

a)

b)

c)

d)

Step-by-step explanation:

a) If the coins are all the same, we have a combination of 35 identical coins in 5 persons.

The amount of combinations is

being n the number of coins and r the number of grandchildren.

b) If the coins are different, the number of combinations can be calculated as:

c) If the coins are all the same, and each grandchild gets the same number of coins, there is only one combination for that (everyone gets 35/5=7 coins)

d)  If the coins are all distinct, but each of the grandchildren get the same numer of coins, the expression to calculate this is:

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."