Question and Answers Forum

All Questions      Topic List

Permutation and Combination Questions

Previous in All Question      Next in All Question      

Previous in Permutation and Combination      Next in Permutation and Combination      

Question Number 120209 by benjo_mathlover last updated on 30/Oct/20

Peter has 12 relatives (5 man & 7 woman)  and his wife also has 12 relatives  (5 woman &7 man). They do not  have common relatives. They decided  to invite 12 guests ,six each of  their relatives, such that there  are six man and six woman   among the guests. How many  ways can they choose 12 guests?

$${Peter}\:{has}\:\mathrm{12}\:{relatives}\:\left(\mathrm{5}\:{man}\:\&\:\mathrm{7}\:{woman}\right) \\ $$ $${and}\:{his}\:{wife}\:{also}\:{has}\:\mathrm{12}\:{relatives} \\ $$ $$\left(\mathrm{5}\:{woman}\:\&\mathrm{7}\:{man}\right).\:{They}\:{do}\:{not} \\ $$ $${have}\:{common}\:{relatives}.\:{They}\:{decided} \\ $$ $${to}\:{invite}\:\mathrm{12}\:{guests}\:,{six}\:{each}\:{of} \\ $$ $${their}\:{relatives},\:{such}\:{that}\:{there} \\ $$ $${are}\:{six}\:{man}\:{and}\:{six}\:{woman}\: \\ $$ $${among}\:{the}\:{guests}.\:{How}\:{many} \\ $$ $${ways}\:{can}\:{they}\:{choose}\:\mathrm{12}\:{guests}? \\ $$

Answered by bemath last updated on 30/Oct/20

  Σ_(k=0) ^5   [ ((5),(k) ) (((    7)),((6−k)) )]^2 = 267 148

$$\:\:\underset{{k}=\mathrm{0}} {\overset{\mathrm{5}} {\sum}}\:\:\left[\begin{pmatrix}{\mathrm{5}}\\{{k}}\end{pmatrix}\begin{pmatrix}{\:\:\:\:\mathrm{7}}\\{\mathrm{6}−{k}}\end{pmatrix}\right]^{\mathrm{2}} =\:\mathrm{267}\:\mathrm{148} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com