If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.
Given Five regular six sided dices are rolled.
From stars and bars the number of n tuples of natural numbers summing up to k is given by
[tex](k-1\\n-1)[/tex]
For k=14 and n=5
[tex](14-1 \\5-1)[/tex]
=[tex](13\\4)[/tex]
=715
Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.
Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:
N=[tex](13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)[/tex]
where last term comes from the 5 tuples containing one 10 and fours'
=715-100-50-20-5
=540
Hence there are 540 such ways which sum to 14 when five six sided dices are rolled.
Learn more about tuples at https://brainly.com/question/12996298
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