Q)

Asked by araima2001 | 29th Nov, 2016, 01:03: PM

Expert Answer:

begin mathsize 16px style There space are space 15 space letters.
straight a comma space straight a comma space straight a comma space straight a comma space straight a comma space straight b comma space straight b comma space straight b comma space straight c comma space straight c comma space straight c space straight d comma space straight e comma space straight e comma space straight f
5 space straight a apostrophe straight s
3 space straight b apostrophe straight s
3 space straight c apostrophe straight s
1 space straight d
2 space straight e apostrophe straight s space
and space 1 space straight f
Total space number space of space arrangements equals fraction numerator 15 factorial over denominator 5 factorial 3 factorial 2 factorial end fraction equals 908107200 space
For space the space 3 space straight c apostrophe straight s space to space be space separated comma space consider space the space 12 space other space letters space arranged space in space straight a space row.
that space is comma space
_a_a_a_a_a_b_b_b_c_c_c_d_e_e_f_
including space places space at space the space beginnning space and space the space end space of space the space row comma space we space must space select space three space positions space to space put
the space straight c apostrophe straight s space from space the space 16 space positions space avaible.
These space three space positions space can space be space chosen space in space 16 straight C subscript 3 space ways equals fraction numerator 16 factorial over denominator 3 factorial 13 factorial end fraction equals fraction numerator 16 cross times 15 cross times 14 over denominator 3 cross times 2 end fraction equals 560
The space other space 12 space letters space could space be space arranged space in space fraction numerator 12 factorial over denominator 5 factorial 3 factorial 2 factorial end fraction equals 6 cross times 11 cross times 10 cross times 9 cross times 8 cross times 7 equals 332640
So comma space the space total space number space of space ways space is space 560 cross times 332640 equals 186278400 space ways end style

Answered by Rebecca Fernandes | 29th Nov, 2016, 07:57: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.