Question Number 13501 by tawa tawa last updated on 20/May/17
$$\mathrm{Find}\:\mathrm{x} \\ $$$$\mathrm{10}_{\mathrm{C}_{\mathrm{x}} } \:=\:\mathrm{5}_{\mathrm{C}_{\mathrm{2}} } \\ $$
Answered by mrW1 last updated on 20/May/17
$$\frac{\mathrm{10}!}{{x}!\left(\mathrm{10}−{x}\right)!}=\frac{\mathrm{5}×\mathrm{4}}{\mathrm{2}×\mathrm{1}}=\mathrm{10} \\ $$$${x}!\left(\mathrm{10}−{x}\right)!=\frac{\mathrm{10}!}{\mathrm{10}}=\mathrm{9}! \\ $$$$\Rightarrow{x}=\mathrm{9}\:\:{or}\:\mathrm{1} \\ $$
Commented by 433 last updated on 20/May/17
$$\&\:{x}=\mathrm{1} \\ $$
Commented by tawa tawa last updated on 20/May/17
$$\mathrm{God}\:\mathrm{bless}\:\mathrm{you}\:\mathrm{sir}.\: \\ $$
Commented by jabbar kutaib last updated on 20/May/17
$$\mathcal{T}{hank}\:{you}\:{mr}. \\ $$
Commented by chux last updated on 20/May/17
$$\&\mathrm{0} \\ $$
Commented by chux last updated on 20/May/17
$$\mathrm{but}\:\mathrm{can}\:\mathrm{you}\:\mathrm{further}\:\mathrm{break}\:\mathrm{this}\: \\ $$$$\mathrm{down}\:\mathrm{to}\:\mathrm{its}\:\mathrm{answers}. \\ $$