Respuesta :
Answer:
a) [tex]82251[/tex]
b) [tex]2.91038 \cdot 10^{24}[/tex]
c) [tex]1[/tex]
d) [tex]3.17746\cdot 10^{21}[/tex]
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
[tex]\binom{n+r-1}{r-1}=\binom{35+5-1}{5-1}=\binom{39}{4}=\frac{39!}{4!35!} =82251[/tex]
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:
[tex]r^n=5^{35}=2.91038 \cdot 10^{24}[/tex]
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:
[tex]\frac{n!}{(n/r)!^r} =\frac{35!}{(35/5)!^5}=\frac{35!}{7!^5}=\frac{1.03331\cdot 10^{40}}{3.25202\cdot 10^{18}} =3.17746\cdot 10^{21}[/tex]
