# Combinatories - Combinatories MCQ

1:

Ramesh has 6 friends. In how many ways can he invite one or more of them at a dinner ?

 A. 61 B. 62 C. 63 D. 64 Answer Report Discuss Option: C Explanation : Click on Discuss to view users comments. Acme said: (1:16pm on Friday 11th January 2013) Would u pls explain? Aditya said: (3:24am on Tuesday 29th January 2013) You seem to be looking for Sum[C[6,n], n=1..6], where C[6,n] = 6!/(n!(6-n!)) is the number of combinations of 6 things taken n at a time.c[6,1]=6!/(1!5!)=6c[6,2]=6!/(2!4!)=15c[6,3]=6!/(3!3!)=20c[6,4]=6!/(4!2!)=15c[6,5]=6!/(5!1!)=6c[6,6]=6!/(6!0!)=1sum[6,15,20,15,6,1]=63 Write your comments here:
2:

The number of ways to arrange th a letters of the  word CHEESE are

 A. 120 B. 240 C. 720 D. 6 Answer Report Discuss Option: A Explanation : Click on Discuss to view users comments. Sreenivasulu.G said: (5:49am on Friday 7th April 2017) 6!/3! = 6Ã—5Ã—4 = 120 Write your comments here:
3:

The number of different permutations of the word BANANA is

 A. 720 B. 60 C. 120 D. 360 Answer Report Discuss Option: B Explanation : Click on Discuss to view users comments. Govendhan said: (1:31am on Wednesday 20th December 2017) 6!/(3!*2!)=60 Write your comments here:
4:

The number n of ways that an organization consisting of twenty -six members can elect a president, treasurer, and secretary (assuming no person is elected to more than one position) is

 A. 15600 B. 15400 C. 15200 D. 15000 Answer Report Discuss Option: A Explanation : The president can be Plected in twenty-six different ways; following this, the treasurer can he elected in twenty-five different ways (since the person chosen president is :-:ot eligible to be treasurer); and following this, the secretary can be elected in twenty-four different ways. Thus, by above principle of counting, there are n = 26 x 25 x 24 = 15 600 different ways in which the organization can elect the officers. Click on Discuss to view users comments. Write your comments here:
5:

Common Data for next 2 questions

There are four bus lines between A and B; and three bus lines between B and C.

The number of ways a person can travel by bus from A to C by way of B will be

 A. 10 B. 12 C. 14 D. 24 Answer Report Discuss Option: B Explanation : There are four ways to go from A to B and three ways to go from B to C. Hence there are 4 x 3 = 12 ways to go from A to C by way of B; Click on Discuss to view users comments. Write your comments here:

X