Itimaal

wax loo adeegsadi Itimaalka.

Ku-tiirsaneyaasha ururka {a.b.c} waxaad u ratibi kartaa lix siyaabood oo kala duwan:

abc	bac	cab
acb	bca	cba

Rattibaad kasta waxay kaga duwantahay tan kale horsiimada ku-tiirsanayaasha.

Raabaqaad waa rattibaad kasta oo ku-tiirsaneyaasha urur la siinayo horsiimo huban.

Abnaqanka n oo loo qoro n! waa taranka tirsiimada laga bilaabo 1 ilaa n taasoo ah:

n! = 1.2.3.4.... (n----3) (n----2) (n----1) n.

Matalan 5! = 1.2.3.4.5. = 120

Ogoow 0! = 1, sidoo kale 1! = 1

Sumadda $n{P}r$ waxay u taagantahay raabaqaad n shey oo markiiba la qaato r shey sida, $8{P}3$ waa tirada raabaqaad 8 shey oo markiiba la qaat qaatay 3 shey.

Tirada raabaqaad n shey oo kala duwan oo markiiba r shey la israacsho waxay la mid tahay

$n{P}r$ n (n -- 1) (n -- 2) . . . (n-- r + 1)

= :${\frac {n}{(n-r)}}_{!}\,$

Haddii r = n

$n{P}r$ = $n{P}n$ = (n -- 2) (n -- 2) .... 3.2.1 = n!

Tusaale

b) :$5{P}1,$ = 5; :$5{P}2,$ = 5.4 = 20; :$5{P}3,$ = 5.4.3 = 60

$5{P}4,$ = 5.4.3.2 = 120

$5{P}5,$ = 5.4.3.2.1 = 120

t) Tirada siyaalaha afar qof ay ugu fariisan karaan 6 kursi waa

$6{P}4,$ = 6.5.4.3 = 360

j) Imisa siyaabood ayaa loo safi karaa shan buug oo kala duwan? taasi waxay ka dhigantahay tirada raabaqaadka shan buug oo la qaato markiiba 5, ama :$5{P}5,$ waa imisa?

$5{P}5,$ = 5! = 5.4.3.2.1 = 120