Practicing Success
Four tickets are marked 00, 01, 10 and 11 respectively, are placed in a bag. A ticket is drawn at random five times, being replaced each time. The probability that the sum of the numbers on the five tickets drawn is 24, is |
$\frac{25}{256}$ $\frac{25}{512}$ $\frac{25}{1024}$ $\frac{25}{128}$ |
$\frac{25}{512}$ |
We have, Number of ways of drawing five tickets = $4 ×4×4×4×4=4^5$ So, total number of elementary events = $4^5$ Now, Favourable number of elementary events = Number of ways of getting 24 as the sum of the numbers on the five tickets. = Coefficient of $x^{24}$ in $(x^0+x^1 +x^{10}+x^{11})^5$ = Coefficient of $x^{24}$ in $(1 + x)^5 (1+x^{10})^5$ = Coefficient of $x^{24}$ in $(1 + x)^5 ({^5C}_0 + {^5C}_1 x^{10}+{^5C}_2 x^{20}+...)$ =$ {^5C}_2 $× Coefficient of $x^4$ in $(1 + x)^5={^5C}_2 × {^5C}_4=50$ |