Probability Practice Test 2

Total number of 5 digit numbers obtained by the digits 1, 2, 3, 4, 5, 6 and 8.
${=}^7{\mathit{P}}_5=7.6.5.4.3=2520$
There are 4 even digits (2, 4, 6 and 8).
∴ 2 even digits can be selected in ${}_{}^4{\mathit{C}}_2^{}=6$ ways
∴ The two ends can be filled in 2 × 6 =12 ways
Remaining 3 places from remaining 5 digits can be filled in ${}_{}^5{\mathit{P}}_3^{}=60$ ways.
Hence, the required probability $=\frac{12\times 60}{2520}=\frac{2}{7}.$