From a class of 15 students, 10 are to chosen for a picnic. There are

1.	From a class of 15 students, 10 are to chosen for a picnic. There are two students who decide that either both will join or none of them will join. In how many ways can the picnic be organized?
Answer» Case 1: Both join In case both the students decide to join, ¹³C₈ × ²C₂ ways = ¹³C₈ = \(\frac{13!}{8!\space5!}=1287\) Case 2: In case none of them join, it will be ¹³C₁₀ Ways 13C₁₀ = \(\frac{13!}{3!\space10!}=286\) Total number of cases are = ¹³C₈ + ¹³C₁₀ 1287 + 286 = 1573

From a class of 15 students, 10 are to chosen for a picnic. There are two students who decide that either both will join or none of them will join. In how many ways can the picnic be organized?

Answer»

Case 1: Both join

In case both the students decide to join,

¹³C₈ × ²C₂ ways = ¹³C₈ = \(\frac{13!}{8!\space5!}=1287\)

Case 2: In case none of them join,

it will be ¹³C₁₀ Ways 13C₁₀ = \(\frac{13!}{3!\space10!}=286\)

Total number of cases are = ¹³C₈ + ¹³C₁₀

1287 + 286 = 1573