Question:
There are \(4\) oranges, \(5\) apples, \(7\) mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is
There are \(4\) oranges, \(5\) apples, \(7\) mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is
Show Hint
If an item can be selected from \(0\) to \(n\) times, then the number of choices is
\[
n+1.
\]
When the question asks for “at least one”, subtract the empty selection at the end.
Updated On: Jun 24, 2026
- \(210\)
- \(240\)
- \(209\)
- \(239\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Find the number of choices for oranges.
Since there are \(4\) oranges, the number of oranges selected can be \[ 0,1,2,3,4 \] Hence, the number of choices is \[ 5 \]
Step 2: Find the number of choices for apples.
Since there are \(5\) apples, the number of apples selected can be \[ 0,1,2,3,4,5 \] Hence, the number of choices is \[ 6 \]
Step 3: Find the number of choices for mangoes.
Since there are \(7\) mangoes, the number of mangoes selected can be \[ 0,1,2,3,4,5,6,7 \] Hence, the number of choices is \[ 8 \]
Step 4: Apply multiplication principle.
Total number of selections: \[ 5\times 6\times 8 \] \[ =240 \] This includes the case where no fruit is selected.
Since at least one fruit must be selected, subtract \(1\): \[ 240-1=239 \]
Step 5: Final conclusion.
Therefore, \[ \boxed{239} \]
Since there are \(4\) oranges, the number of oranges selected can be \[ 0,1,2,3,4 \] Hence, the number of choices is \[ 5 \]
Step 2: Find the number of choices for apples.
Since there are \(5\) apples, the number of apples selected can be \[ 0,1,2,3,4,5 \] Hence, the number of choices is \[ 6 \]
Step 3: Find the number of choices for mangoes.
Since there are \(7\) mangoes, the number of mangoes selected can be \[ 0,1,2,3,4,5,6,7 \] Hence, the number of choices is \[ 8 \]
Step 4: Apply multiplication principle.
Total number of selections: \[ 5\times 6\times 8 \] \[ =240 \] This includes the case where no fruit is selected.
Since at least one fruit must be selected, subtract \(1\): \[ 240-1=239 \]
Step 5: Final conclusion.
Therefore, \[ \boxed{239} \]
Was this answer helpful?
0
0
Top AP EAPCET Mathematics Questions
- $D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$
- $f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is
- Consider the following lists.
List-I List-II (A) $f(x) = \frac{|x+2|}{x+2} , x \ne -2 $ (I) $[\frac{1}{3} , 1 ]$ (B) $(x)=|[x]|,x \in [R$ (II) Z (C) $h(x) = |x - [x]| , x \in [R$ (III) W (D) $f(x) = \frac{1}{2 - \sin 3x} , x \in [R$ (IV) [0, 1) (V) { -1, 1} - If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$. then the system of three equations $2x + 3 | y | + 5[z] = 0, x + |y| - 2[z] = 4, x + |y| + |z| = 1$ has
- Investigate the values of $\lambda$ and $\mu$ for the system $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\lambda z=\mu$ and match the values in List - I with the items in List - II.
List I List II (A) $\lambda=8, \mu \neq 15$ 1. Infinitely many solutions (B) $\lambda \neq 8, \mu \in R$ 2. No solution (C) $\lambda=8, \mu=15$ 3. Unique solution
View More Questions
Top AP EAPCET Combinations Questions
- The number of six-digit natural numbers that can be formed with the digits 2, 3, 4, 0, 5, 6, 7, 8 is:
- The number of ways in which a committee of 7 members can be formed from 6 teachers, 5 fathers and 4 students in such a way that at least one from each group is included and teachers form the majority among them, is:
- If $^{n}C_{12} = ^{n}C_{8}$, then $^{n}C_{17} =$
- A student is to answer \(10\) out of \(13\) questions in an examination such that he must choose at least \(4\) from the first \(5\) questions. The number of choices available to him is:
- The least value of \(n\) so that \[ {}^{\,n-1}C_3+{}^{\,n-1}C_4\gt {}^{\,n}C_3 \] is
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions