Advertisements
Advertisements
प्रश्न
In how many ways can a student choose 5 courses out of 9 courses if 2 courses are compulsory for every student?
उत्तर
We are given that 2 courses are compulsory out of the 9 available courses,
Thus, a student can choose 3 courses out of the remaining 7 courses.
Number of ways =\[{}^7 C_3 = \frac{7!}{3! 4!} = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} = 35\]
APPEARS IN
संबंधित प्रश्न
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Prove that
A person wants to buy one fountain pen, one ball pen and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?
From Goa to Bombay there are two roots; air, and sea. From Bombay to Delhi there are three routes; air, rail and road. From Goa to Delhi via Bombay, how many kinds of routes are there?
A mint prepares metallic calendars specifying months, dates and days in the form of monthly sheets (one plate for each month). How many types of calendars should it prepare to serve for all the possibilities in future years?
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
Evaluate the following:
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If 16Cr = 16Cr + 2, find rC4.
If α = mC2, then find the value of αC2.
From 4 officers and 8 jawans in how many ways can 6 be chosen. to include at least one officer?
A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?
Find the number of (ii) triangles
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
Find the number of ways in which : (a) a selection
A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve?
(a) 6
(b) 20
(c) 60
(d) 120
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 15C4
Find the value of 20C16 – 19C16
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has at least one boy and one girl
The number of ways in which a team of eleven players can be selected from 22 players always including 2 of them and excluding 4 of them is ______.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
