

View Answer
Shortcut:
From 'a' persons of a group X and 'b' persons from group Y, the number of ways in which 'n' persons can be chosen to include exactly 'p' persons of group X and the rest of group Y is given by
(^{a}C_{p} x ^{b}C_{n − p}) ways
Here, a = 4, b = 8, n = 6, p = 1
Using the value in the shortcut, we get:
Required ways = ^{4}C_{1} x ^{8}C_{5} + ^{4}C_{2} x ^{8}C_{4} + ^{4}C_{3} x ^{8}C_{3} + ^{4}C_{4} x ^{8}C_{2}
=
4!
/
1!(4 − 1)!
x
8!
/
5! x (8 − 5)!
+
4!
/
2!(4 − 2)!
x
8!
/
4! x (8 − 4)!
+
4!
/
3!(4 − 3)!
x
8!
/
3! x (8 − 3)!
+
4!
/
4!(4 − 4)!
x
8!
/
2! x (8 − 2)!
=
4!
/
3!
x
8!
/
5! x 3!
+
4!
/
2! x 2!
x
8!
/
4! x 4!
+
4!
/
3! x 1!
x
8!
/
3! x 5!
+
4!
/
4! x 0
x
8!
/
2! x 6!
= 224 + 420 + 224 + 28 = 896
Hence, we can choose in 896 ways.

