# Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be - Mathematics and Statistics

Sum

Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.

#### Solution

 Train Car Number of outcomes No. of friends 3 6 ""^9"C"_3 4 5 ""^9"C"_4 5 4 ""^9"C"_5 6 3 ""^9"C"_6

Required number = ""^9"C"_3 + ""^9"C"_4 + ""^9"C"_5 + ""^9"C"_6

= (""^9"C"_4 + ""^9"C"_3) + (""^9"C"_6 + ""^9"C"_5) = ""^10"C"_4 + ""^10"C"_6

= (10!)/(6!4!) + (10!)/(4!6!)

= 210 + 210
= 420

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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Miscellaneous Exercise 6 | Q 12 | Page 92