(i) The value of [tex]_9C_9[/tex] is 1
(ii) The value of [tex]_{10}P_4[/tex] is 5040
Explanation:
(i)Given that the combination is [tex]_9C_9[/tex]
We need to evaluate the combination [tex]_9C_9[/tex]
The formula to find the combination is given by
[tex]_nC_r=\frac{n!}{(n-r)!r!}[/tex]
Let us use this formula to evaluate [tex]_9C_9[/tex]
Thus, we have,
[tex]_9C_9=\frac{9!}{(9-9)!9!}[/tex]
Simplifying, we have,
[tex]_9C_9=\frac{9!}{(0)!9!}[/tex]
Cancelling the terms, we get,
[tex]_9C_9=1[/tex]
Thus, the value of [tex]_9C_9[/tex] is 1
(ii) Also, given that the permutation [tex]_{10}P_4[/tex]
We need to evaluate the permutation [tex]_{10}P_4[/tex]
The formula to find the permutation is given by
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]
Let us use this formula to evaluate [tex]_{10}P_4[/tex]
Thus, we have,
[tex]_{10}P_4=\frac{10!}{(10-4)!}[/tex]
Simplifying, we get,
[tex]_{10}P_4=\frac{10!}{6!}[/tex]
Expanding, we get,
[tex]_{10}P_4=\frac{10\times9\times8\times7\times6!}{6!}[/tex]
Cancelling the common terms, we get,
[tex]_{10}P_4=10\times9\times8\times7[/tex]
simplifying, we get,
[tex]_{10}P_4=5040[/tex]
Thus, the value of [tex]_{10}P_4[/tex] is 5040
