STEP - BY - STEP EXPLANATION
What to find?
The number of ways to get 10 tails.
Given:
Number of time the coin is tosses(n) =25
and r=10 ; 10 tails (getting tails success and heads failure).
Since, the number of tosses is 25 and we want to get 10 tails, then we can solve this using combination.
Step 1
Recall the combination formula.
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]n= 25 r=10
Step 2
Substitute the values into the formula and simplify.
[tex]25C_{10}=\frac{25!}{(25-10)!10!}[/tex][tex]=\frac{25!}{15!\times10!}[/tex][tex]=\frac{25\times24\times23\times22\times21\times20\times19\times18\times17\times16\times15!}{15!\times10!}[/tex][tex]=\frac{25\times24\times23\times22\times21\times19\times18\times17\times16}{10\times9\times8\times7\times6\times5\times4\times3\times2}[/tex][tex]=3268760[/tex]ANSWER
3268760 ways.
