Question

A picnic party of 10 persons to-go by two Vechicles one matador with a seating capacity of.8 and a Maruti car with a seating capacity of 4. In how many ways can the travel arrangements he made?

Answer 1

A(8)	10	B(4)
8		2
7		3
6		4

Total no ways
$=({}^{10}{C}_8\times {}^2{C}_2)+({}^{10}{C}_7\times {}^3{C}_3)+({}^{10}{C}_6\times {}^4{C}_4)$
${=}^{10}{C}_2+{}^{10}{C}_3+{}^{10}{C}_4({\therefore }^{10}{C}_6={}^{10}{C}_4)$
$\frac{10\cdot 9}{1\cdot 2}+\frac{10\cdot 9\cdot 8}{1\cdot 2\cdot 3}+\frac{10\cdot 9\cdot 8\cdot 7}{1\cdot 2\cdot 3\cdot 4}$
We
could write the answer straight away by
following Rule (o), P. 293 of division into groups.
$\frac{10!}{8!2!}+\frac{10!}{7!3!}+\frac{10!}{6!4!}$