Question

A person tosses a coin 25 times. In how many ways can he get 10 tails?

Answer 1

In a series of 'n' independent trails, the number of 'r' successes and 'n-r' failures can happen in $\fn_jvn \small \binom{n}{r}$ ways, since that is equal to the number of combinations of 'n' things taken 'r' at time

Apply the above

We have 25 times coin is tossed i.e n=25

and r=10 ; 10 tails (gettting tails success and heads failure)

So no. ways a person gets 10 tails out f 25 tosses = $\fn_jvn \small \binom{25}{10}$ = 3268760

$\fn_jvn \small \binom{25}{10} = \frac{25x24x23x22x21x20x19x18x17x16}{1x2x3x4x5x6x7x8x9x10}$

$\fn_jvn \small = \frac{11861676288000 }{3628800} = 3268760$