A) \[^{22}{{P}_{10}}\]
B) \[^{22}{{P}_{11}}\]
C) \[^{22}{{P}_{13}}\]
D) None of these
Correct Answer: C
Solution :
[c] Consider the equation \[a+b=10\] number of solutions of this equation is \[^{10+2-1}{{C}_{2-1}}=11.\] Next equation is \[a+b+c+d=21\] hence \[c+d=11\] and number of solution of this equation is 12. Similarly for third equation \[a+b+c+d+e+f=33\] or \[e+f=12\] or number of solution is 13. Similarly for last equation \[a+b+c+d+...+x+y+z=208,\] or \[y+z=22\] or number of solution is 23. Required number of ways is \[11\times 12\times 13\times ...\times 21\times 22\times 23=\frac{23!}{10!}{{=}^{23}}{{P}_{13}}\]
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