Question

de quantas formas podemos representar o numero 15 como soma de varios numeros naturais?

Answer 1

Observe ==>**| ..anagrama=3!2!=3 formas ... **| ou *|* ou |**

x+y=15 ==> ***********|*** ==>anagrama =15!/14!

x+y+z=15 ==> **|*********|*** ==>anagrama =15!/13!2!

x+y+z+t=15 ==> **|****|*****|*** ==>anagrama =15!/12!3!

x+y+z+t+w=15 ==> **|****|**|***|*** ==>anagrama =15!/11!4!

x+y+z+t+w+v=15 ==> **|*|***|**|***|*** ==>anagrama =15!/10!5!

x+y+z+t+w+v+y=15 ==> **|*|***|**|**|*|*** ==>anagrama =15!/9!6!

x+y+z+t+w+v+y+a=15 ==> **|*|***|**|*|*|*|*** ==>anagrama =15!/8!7!

a partir daqui basta multiplicar por dois, o número de anagramas será o

mesmo....

2 * ( 15!/14!+(15!/13!2!)+15!/(12!3!)+15!/(11!4!)+15!/(10!5!)+15!/(9!6!)+15!/(8!7!))

=32766 formas