We know that if
![\[^{n}{{C}_{p}}~={{~}^{n}}{{C}_{q}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-13763231cb22f1990bdd6e1dc8270662_l3.png "Rendered by QuickLaTeX.com")
then one of the following conditions need to be satisfied:
![\[\left( i \right)\text{ }p\text{ }=\text{ }q\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6cd7efaf7aaee0ebc3c0fb48e086f872_l3.png "Rendered by QuickLaTeX.com")
![\[\left( ii \right)\text{ }n\text{ }=\text{ }p\text{ }+\text{ }q\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8c17cbab1407e0bfd6b2e2766c86592a_l3.png "Rendered by QuickLaTeX.com")
So from the question
![\[^{n}{{C}_{12}}~={{~}^{n}}{{C}_{5}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7055ac4a3a173292656c0f215a27c8aa_l3.png "Rendered by QuickLaTeX.com")
we can say that
![\[12\text{ }\ne \text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a146628b71e37b593d6b4efd7cd3f807_l3.png "Rendered by QuickLaTeX.com")
So, the condition (ii) must be satisfied,
![\[n\text{ }=\text{ }12\text{ }+\text{ }5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-df0f996f9bf3cce07fb5b91e059bcaad_l3.png "Rendered by QuickLaTeX.com")
![\[n\text{ }=\text{ }17\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-16af1b758b9fdf8b5a3a35c81459dfe1_l3.png "Rendered by QuickLaTeX.com")
∴ The value of
![\[n\text{ }is\text{ }17\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a397d9e41dc04ed00a1b311d595820ce_l3.png "Rendered by QuickLaTeX.com")
We know that if
then one of the following conditions need to be satisfied:
So from the question
we can say that
So, the condition (ii) must be satisfied,
∴ The value of
