Respuesta :
We are given 8 h's and 2 t's.
A permutation of these letters is simply an arrangement in a row.
For example:
h h h t h h t h h h
or
h t h h h h h h t h
The number of arrangements is equal to the number of pairs of positions we fix for t, the rest of the positions are filled with h:
these positions are :
(1, 2), (1, 3), (1,4)..... (1, 10)
(2, 3), (2,4)..... (2, 10)
(3,4).... (3,10)
(9,10)
so the 1st position combined with any of the remaining 9
the 2 position combined with any of the remaining 8
...
the 9th position combined with the remaining 1
this makes 9+8+7+6+5+4+3+2+1=45 positions to place the 2 t's.
Remark: the number of positions for the 2 t's could also have been calculated by C(10, 2)=10!/(8!2!)=(10*9)/2=45
Answer: 45
A permutation of these letters is simply an arrangement in a row.
For example:
h h h t h h t h h h
or
h t h h h h h h t h
The number of arrangements is equal to the number of pairs of positions we fix for t, the rest of the positions are filled with h:
these positions are :
(1, 2), (1, 3), (1,4)..... (1, 10)
(2, 3), (2,4)..... (2, 10)
(3,4).... (3,10)
(9,10)
so the 1st position combined with any of the remaining 9
the 2 position combined with any of the remaining 8
...
the 9th position combined with the remaining 1
this makes 9+8+7+6+5+4+3+2+1=45 positions to place the 2 t's.
Remark: the number of positions for the 2 t's could also have been calculated by C(10, 2)=10!/(8!2!)=(10*9)/2=45
Answer: 45
