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Question: From 4 officers and 8 jawans, the number of ways to choose 6 so as to include at least one officer i...

From 4 officers and 8 jawans, the number of ways to choose 6 so as to include at least one officer is equal to

A

924

B

896

C

224

D

None

Answer

896

Explanation

Solution

4 officers and 8 jawans at least one officers

= 4C18C5+4C28C4+4C38C3+4C48C24{C_{1}}^{8}C_{5} +^{4}{C_{2}}^{8}C_{4} +^{4}{C_{3}}^{8}C_{3} +^{4}{C_{4}}^{8}C_{2}